True of False

Question 1

If V is an inner product space with an inner product <x|y>, and if x,y is an element of V are two non zero vectors where <x|2y> = 0, then x and y are parellel

Answer 1

F

Question 2

If V is a real inner product space with an inner product <x|y>, then <x|2y-3z>= 2<x|y> - 3<x|z> for all x, y, z is a element of V

Answer 2

T

Question 3

If x = (1,2,3) and y =(-3,0,1), then x and y are orthogonal using the standard inner product <|> for R^3x1

Answer 3

T

Question 4

The angle between x = (1,1,1) and y = (1,1,-2), is +- pi/2 radians using the standard inner product <|> for R^3x1

Answer 4

T

Question 5

The set {(1,0,1),(1,0,-1),(0,1,0)} is an orthonormal basis for R^3x1 using the standard inner product <|> for R^3x1

Answer 5

F

Question 6

Let S = {x1,x2,x3,…,xn} be a Linearly Dependent set of vectors in R^nx1. The Gram Schmidt process applied to S must produce a basis for R^n*1

Answer 6

F

Question 7

Anxn is a nonsingular iff det(A)=/0

Answer 7

T

Question 8

Let A be a 4x4 matrix where det(A) = 3, then the rank(A) = 4

Answer 8

T

Question 9

Let A and B be nxn matricies. If det(AB) = 0, then det(A) = 0 or det(B) = 0

Answer 9

T

Question 10

Let A and B be nxn matricies. If det(A)/=0, then det(A^-1BA) = det(B)

Answer 10

T

Question 11

Let A and B be nxn matrices, then det(A+B) = det(A) + det(B)

Answer 11

F

Question 12

A = {(1,1)(0,2)} has eigenvalues lamda = 1 and lamda = 2

Answer 12

T

Question 13

Let A be a nxn nonsingluar matrix lamda is an eigenvalue of A iff 1/lamda is an eigenvalue of A^-1

Answer 13

T

Question 14

If each eigenvalue of A is repreated exavtly once, then A is always diagonalizable

Answer 14

T

Question 15

Let A be a nxn matrix. For each and every lamda that is a vlue of sigma(A), it is always true that: Geo multa(lamda) <= alg multA(lambda)

Answer 15

T

Question 16

Let A = {(2,0)(1,2)} with eigenvalue lamda = 2. Then A is diagonalizable

Answer 16

F