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MA 351 Exam 2 T/F

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Section 1

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Let A, B, C be respectively 3x2, 2x3, and 3x3 matrices. Then A(BC), B(CA) and B(AC) are all defined

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Mar 1, 2020

Cards (46)

Section 1

(46 cards)

Let A, B, C be respectively 3x2, 2x3, and 3x3 matrices. Then A(BC), B(CA) and B(AC) are all defined

Front

false

Back

suppose the A is an m x n matrix such that AXC = B has a solution for all B in Rm. then the solution AtX = B', when it exists, is unique

Front

true

Back

Suppose that A and B are n x n matrices such that AB is invertible Then both A and B are invertible

Front

true, rank(AB) must be lower

Back

Suppose that A is a 3x7 matrix such that the equation AX=B is solvable for all B in R3. Then A has rank 3

Front

true

Back

Suppose that A is an n x n invertible matrix and B is any n x n matrix. Then ABA^-1 = B

Front

false AA^-1B=B

Back

Suppose that S={X1X2X3X4X5} spans a 4-D subspace W of R7. The S contains a basis for W

Front

true

Back

Suppose that A is an n x n matrix that satisfies A^2 +7A - I =0. Then A is invertible

Front

true

Back

{[11],[12],[47]} spans R2

Front

true

Back

A linear transformation if R2 into R2 that transforms [1,2] to [7,3] and [3,4] to [-1,1] will also transform [5,8] to [13, 7]

Front

ture

Back

Suppose that S= {w1,w2,w3,w4,w5} spans a 4-dim vector space W of R7. Then S contains a basis for W

Front

true

Back

Suppose A is an invertible matrix and B is any matrix for which BA is defined. Then BA and B need not have the same rank

Front

false they must have the same rank

Back

suppose that A is a matrix for which the column space and null space are both 2 dim. Then A must be a 4x4 matrix

Front

false

Back

Assume that A and B are matrices such that AB is defined and the columns of B are linearly dependent. Then the columns of AB are also linearly dependent

Front

True

Back

Suppose that A is an m x n matrix such that AX =B has a solution for all B in Rm. the the solution AtX=B' , when it exists, is unique

Front

Truerank(A)=rank(At)=m

Back

All transformations of R2 into R2 transform line segments onto line segments

Front

false

Back

Suppose that T is a linear transformation of R2 into itself and I know what T transforms [1,1] and [2,3] to. Then I can compute the effect of T on any vector

Front

true

Back

Assume that A and B are matrices such that AB is defined and AB has a column that has all its entries equal to 0. Then one of the columns of B also has all its entries equal to 0.

Front

false

Back

Let A be a 4x3 matrix and B s 3x4 matrix. Then AB cannot be invertible

Front

true rank(AB)<rank(B)<3

Back

Suppose that A is an n x n matrix such that AAt = I. Then AtA = I as well

Front

true, At must be A^-1

Back

Suppose that A is an m x n matrix such that the solution to AtX=B', when it exists is unique. Then AX=B has a solution for all B in Rm

Front

TrueA is m x n At is n x m rank(At)=m

Back

If A and B are 2x2 matrices (AB)^2 = A^2B^2

Front

false (AB)^2 = ABAB A^2B^2 = AABB

Back

Suppose that W is a 4-D subspace of R7 that is spanned by {X1X2X3X4} then one of the Xi must be a linear combination of the others

Front

false

Back

The null space of a non zero 4x4 matrix cannot constrain a set of 4 linearly independent vectors

Front

true

Back

Let W be a two-dimensional subspace of R3. Then 2 of the following 3 vectors span W: X=[100] Y=[010] Z=[001]

Front

False

Back

It is impossible for a linear transformation from R2 into R2 to transform a parallelogram onto a square

Front

false

Back

Suppose that S= {w1,w2,w3,w4,w5} spans a 4-dim vector space W of R7. Then {w1,w2,w3,w4} also spans W

Front

false

Back

Lat A be a 4 x 3 matrix and B a 3 x 4 matrix. Then AB cannot be invertible

Front

true

Back

Suppose that W is a 4-D subspace of R7 and X1 X2 X3 X4 are vectors that belong to W. then {X1X2X3X4} spans W

Front

false

Back

suppose A is a 3 x 7 matrix such that the equation Ax = B is solvable for all B in R3. Then Rank(A) = 3

Front

true

Back

Assume A and B are matrices such that AB is defined and A has a row of all entries equal to 0. Then one of the rows of AB has all entries equal to 0.

Front

true

Back

Suppose that all of the row vectors of the matrix A are linearly independent. Then A is invertible

Front

false

Back

It is impossible for a linear transformation from R2 into R2 to transform a parallelogram onto a square

Front

false

Back

Suppose that A is an m x n matrix such that AX =B has a solution for all B in Rm. the the solution AtX=B' has a solution for B' in Rn

Front

FalseRank(A)=m Rank(At)=n

Back

Suppose that A is invertible and B is row equivalent to A. Then B is invertible

Front

true

Back

Assume A and B are matrices such that AB is defined and B has a column that has all its entries equal to 0. Then one of the columns of AB has all its entries equal to 0

Front

true

Back

Suppose that A is a 4x9 matrix such that the column space of A is a line in R4. Then every row of A is a multiple of the first row given that the first row is non zero

Front

true

Back

Suppose A is an invertible matrix and B is any matrix for which AB is defined then the matrices AB and B need not have the same rank

Front

false they must have the same rank

Back

Suppose that matrices A and B satisfy AB=0. Then either A=0 or B=0

Front

false

Back

Let A=Rpi/2 be the matrix that describes rotation by pi/2 radians. Then A^4 = I where I is the 2x2 identity matrix

Front

true 360 degree rotation

Back

Suppose {X1X2X3X4X5} spans a 4-D vector space W of R7. Then {X1X2X3X4} also spans W

Front

false

Back

Assume that A and B are matrices such that AB is defined and the rows of A are linearly dependent. Then the rows of AB are also linearly dependent

Front

true

Back

Suppose that A is a matrix for which the column space and null space are both 2 dimensional. Then A must be a 4x4 matrix

Front

Falserank(a)=null(A)=2 n=rank+null=4must be mx4 matrix

Back

Suppose that A is invertible and B is any matrix such that AB is defined. Then AB and B have the same nullspace

Front

True

Back

Suppose that A and B are n x n matrices that both have linearly independent columns. Then A and B have the same RREF

Front

true

Back

It is impossible for a linear transformation from R2 into R2 to transform a parallelogram onto a pentagon

Front

true

Back

Suppose that {X1X2X3X4X5} spans a 4-D subspace W of R7. Then one of the Xi must be a linear combination of the others

Front

true

Back