Some Review Problems for Linear Algebra and Linear Transformations.

1. Suppose that


Which of these subsets of the vector space R4 are subspaces?

A. NoneB. X only C. Y and Z only
D. X, Y, and Z E. None of these

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2. Let

Which of the follwing matrices represents the composition T1(T2) with respect to the standard bases for R2 .

A.

B.

C.

D.

E.

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3. If b is not 0 and ad-bc is not 0 then


A. -2B. -2b C. 0D. 2b E. 2

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4. Suppose T: R3 -> R3 is the linear transformation defined by


Which is the following is equal to


A

B

C

D

E

does not exist

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5. Which of the vectors


are orthogonal to the vector

and have length less than 4?

A. y onlyB. z only C. x and y only D. x and z only E. None of these

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6. What is the value of c for which the vectors


are orthogonal?

A. -5/7B. -4/7 C. -3/7D.-2/7 E. -1/7

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7. If

what is the determinant of S-1?

A. -2
B. -1/2
C. 1/4
D. 1/2
E. 2

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8. Which of the following is a necessary and sufficient condition for the vector


to belong to the subspace of R3 generated by the vectors


A. a - 3 b -4 c = 0 B. 2 a -4 b - 3 c = 0 C. 3a - 2 b - 2 c = 0
D. 4 a - 3 b -2 c = 0 E. 5 a - 7 b - c = 0.

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9. Let T: R2 -> R2 be defined by


Which of the following is an equation of the line that is mapped onto itself by T?

A. y-x = 0B. 2 x + y = 0 C.-x+4y = 0 D. x + 2 y = 0E. 4 x - y = 0

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10. What is the kernel of the linear transformation


A

B.

C.

D.

E.

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11. What is the inverse of the matrix


A

B.

C.

D.

E.

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