True or false for each question xam2 November 2, 2015 (four pages in total) . An

Question

True or false for each question xam2 November 2, 2015 (four pages in total) . An Name: You may not use calculators, laptops, books or notes. Please show all of your work answer without justification will receive little credit. (1) ( 16 x 2 pts) Let A, B. C, P be square matrices. Circle true (T) or false (F): no seed for justification for this problem. a) (T/F) For a 4 × 7 matrix A, Nul(A) is a linear subspace of R. b.), (T/F) For a 4 × 7 matrix A, Col(A) is a linear subspace of R7 c.) (T/F) If W span {ul.. , , ,%), then din(W)-m. d.) (T/F) The columns of an invertible n x n matrix A may not form a basis for R e.) (T/F) Im are linearly dependent then t.... , Um are also linearly dependent. f) (T/F) A linear map from R" to R defined by a matrix C is a injective iff C is g) (T/F) A linear map from R" to R" defined by a matrix C is a onto iff det(C)0. h) (T/F) Suppose A = PB where P is invertible. Then the columns of A are inde- invertible. pendent iff the columns of B are independent. pendent iff the columns of B are independent always linearly dependent. i.) (T/F) Suppose A- BP where P is invertible. Then the columns of A are inde- J) (T/F) Suppose A BP where P is not invertible. Then the columns of A are k) (T/F) Suppose b is a nonzero vector. Then the solutions z of Az = b form a L) (T/F) For an m × n matrix M of rank r, its column span has dimension m-r. linear subspace. m) (T/F) For an m × n matrix M of rank r, its null space has dimension m-r. n) (T/F) Let u be the zero vector. Since A-6e, we conclude that 6 is an eigen- value of A o.) (T/F) A is invertible iff 0 is not an eigenvalue of A. p.) (T/F) Matrices of a linear map (from R" to R") under different bases are differ- ent, hence may have different eigenvalues.

Explanation / Answer

A. .true

B...false

C...false

D...false

E...false

F...true

G...true

H...true

I...true

J...true

K...false

L...false

M...false

N...false

O...true

P...false

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