jaffer (dsj398) – HW7 – caputo – (56555)

jaffer (dsj398) – HW7 – caputo – (56555) 1

This print-out should have 5 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. Problem 1 is worth 0 points and it is not a

multiple choice problem. Problem 1 will be in the next Quiz.

001 0.0 points

This question will not be graded as part of Homework 3. It will be one of the questions on Quiz 3.

Let T : R2 → R2 be a linear transformation such that

T(x) = x1u + x2v, x =

[

x1 x2

]

,

where

u =

[

2 −3

]

, v =

[

−4 1

]

.

Find the Standard Matrix A for T .

1. A =

[

2 −4 −3 1

]

002 5.0 points

Every elementary row operation on a ma- trix is reversible.

True or False?

1. TRUE

2. FALSE

003 5.0 points

The columns of a matrix A are linearly independent if the equation Ax = 0 has the trivial solution.

True or False?

1. FALSE

2. TRUE

004 5.0 points

If A is a 4 × 3 matrix and T is the Ma- trix Transformation T : x → A x, then the domain of T is R3.

True or False?

1. FALSE

2. TRUE

005 10.0 points

If T : R2 → R2 is the linear transformation such that

T

([

x1 x2

])

= x1

[

−1 2

]

+ x2

[

−2 1

]

,

determine T(x) when x =

[

3 1

]

.

1. T(x) =

[

−4 7

]

2. T(x) =

[

−5 7

]

3. T(x) =

[

3 1

]

4. T(x) =

[

−4 6

]

5. T(x) =

[

−5 6

]