MATH 313

Question 1

(A + B)' = A' + B'?

Answer

true

Question 2

If A -> I, A invertible?

Answer

true

Question 3

A subspace is a vector space?

Answer

true

Question 4

A single vector by itself is linearly dependent?

Answer

true

Question 5

R2 is a subspace of R3?

Answer

true

Question 6

The nullspace of a matrix is a vector space?

Answer

true

Question 7

A plane in R3 is a two-dimensional subspace of R3?

Answer

true

Question 8

# of pivots = dimension of columnspace?

Answer

true

Question 9

If c is in V and if B contains n vectors, the the B-coordinate vector is in Rn?

Answer

true

Question 10

A and B are nxn. If the columns of A span Rn, then det(A) = 0?

Answer

true

Question 11

A and B are nxn. det(A) = product of diagonal entries of A?

Answer

true

Question 12

A and B are nxn. det(A + B) = det(A) + det(B)?

Answer

true

Question 13

A, P, D nxn matrices. Elementary Row Operations of A don't change det(A)?

Answer

true

Question 14

A, P, D nxn matrices. IF AP = PD, with D diagonal, then the nonzero columns of P must be the eigenvectors of A?

Answer

true

Question 15

A, P, D nxn matrices. If A is diagonalizable, then A has n distinct eigenvalues?

Answer

true

Question 16

A is nxn. Ax = b has a solution for ever b in Rn iff A -> I?

Answer

true

Question 17

[a1 a2 a3 b] is consistent iff A = {a1, a2, a3, b}?

Answer

true

Question 18

A 4x3 matrix can have at most 3 pivot terms?

Answer

true

Question 19

If A is a matrix for which Au = b and Av = 0, then A(2u + v) = b?

Answer

true

Question 20

Two vectors are linearly dependent if they both lie on the same line that passes through the origin?

Answer

true

Question 21

Let T: Rn -> Rn be a linear transformation. If T is one-to-one, then T must also be onto?

Answer

true

Question 22

If V is n-dimensional vector space, then any collection of n vectors that span V is a basis for V?

Answer

true

Question 23

If B is an 5x7 matrix then the minimal possible dimensions for Nul(B) is zero?

Answer

true

Question 24

A line in R3 is a one-dimensional subspace of R3?

Answer

true

Question 25

P3 is a subspace of P4?

Answer

true

Question 26

If the columns of A span Rn, then det(A) =/= 0?

Answer

true

Question 27

If A is invertible, then A is diagonal?

Answer

true

Question 28

If A has n real eigenvalues, then det(A) is equal to the product of its eigenvalues?

Answer

true

Question 29

If A has n distinct eigenvalues, then A is diagonalizable?

Answer

true

Question 30

If ||u||^2 + ||v||^2 = ||u + v||^2, then u and v are orthogonal?

Answer

true

Question 31

A matrix is invertible if det(matrix) =/= 0.

Answer

true

Question 32

An nxn matrix is diagonalizable if the # of eigenvalues is n

Answer

true

Question 33

A matrix can be not invertible, but diagonalizable

Answer

true

MATH 313

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