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

Crea una cuenta gratis para terminar este test

Preguntas del test (33)

Información

Escríbenos

¿Qué te parece el nuevo diseño?