U. Washington AMATH 352 - Spring 2011

The midterm is Friday April 29th, 2011 in class. It will be 50 minutes: closed book, no notes,

no calculators.

You should know the definitions and the results covered in class and how to use them, including

(but not limited to):

• A norm.

• A linear function.

• Linear combinations.

• A real linear space.

• The vector space Rnand the space of matrices Rm×n

.

• The function spaces C0, C1, Pk.

• A subspace (in particular, that it must be closed under addition and scalar multiplication,

and hence under linear combinations).

• Matrix-vector and matrix-matrix multiplication, as well as addition and scalar multiplication

of vectors and matrices.

• Linear independence.

• A basis for a linear space, the dimension.

• The null space N (A) and range or column space R(A) of a matrix.

• Matrix and vector transpose, AT.

• The Euclidian inner product of vectors u,v ∈ Rm.

• The inverse matrix and the identity matrix.

• If V is a subspace of Rnthen dim(V ) ≤ n.

• If A ∈ Rm×nthen rank(A) ≤ min(m,n) and dim(N (A)) = n− rank(A).

Matlab: You should understand the following:

• Defining row vs. column vectors, transpose of vectors or matrices.

• Colon notation for subarrays of a matrix, e.g. A(:,j) is the jth column and A(2:4,:) is a

3× n matrix consisting of rows 2,3,4 of A ∈ Rm×n.

• The difference between * and .* for vector or matrix multiplication.

• How to read a simple Matlab program involving for loops and interpret the results of a

program.

• I will not ask you to write a Matlab program, but you should be able to read a simple one.

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