linear algebra 1 class notes
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8/2/2019 Linear Algebra 1 Class Notes
1/24
M Dfmdn DpmkLA kb gomzq~a| wgkabga
Amdkc dnn-dpmkdfmdn4>J{dfoo"gom
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
2/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
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8/2/2019 Linear Algebra 1 Class Notes
3/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
4/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
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8/2/2019 Linear Algebra 1 Class Notes
5/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
6/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
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8/2/2019 Linear Algebra 1 Class Notes
7/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
8/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
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8/2/2019 Linear Algebra 1 Class Notes
9/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
10/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
11/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
12/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
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8/2/2019 Linear Algebra 1 Class Notes
13/24
M Dfmdn DpmkLA kb gomzq~a| wgkabga
Amdkc dnn-dpmkdfmdn4>J{dfoo"gom
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
14/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
15/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
16/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
17/24
z n e MdgfkbaK w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
18/24
z n e Mdgfkba
K w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
19/24
z n e Mdgfkba
K w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
20/24
z n e Mdgfkba
K w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
21/24
z n e Mdgfkba
K w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
22/24
z n e Mdgfkba
K w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
23/24
z n e Mdgfkba
K w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
Ha~ {oq|w box$
http://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?clhttp://www.pdfmachine.com/?cl -
8/2/2019 Linear Algebra 1 Class Notes
24/24
z n e Mdgfkba
K w d zn e x | k ~a | ~f d ~ z |onqgaw tqd c k~{ ZNE e k caw x k ~f adwa$
Z|onqga tqdck~{ ZNE ekcaw kb wagobnw dbn z|awa|ua ~fa kb~ah|k~{ oe {oq| o|khkbdc nogqmab~w" Gomzd~klca dg|owwbad|c{ dcc Xkbnoxw zcd~eo|mw# ke {oq gdb z|kb~ e|om d xkbnoxw dzzckgd~kob {oq gdb qwa zneMdgfkba"
H ~ $
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