2018 SECOND SEMESTER TMA2 MTH212 LINEAR ALGEBRA QUESTION AND ANSWER

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Question 1. A square matrix A such that aij=o¥i>j is called?

A. Lower triangular

B. Upper triangular

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C. Strictly upper triangular

D. Strictly lower triangular

Answer is B. Upper triangular

Question 2. Let T€A(A), then T is invertible if on only if the consto term in the minimal polynomial of T is ____?

A. Not zero

B. Zero

C. Not one

D. One

Answer is A. Not zero

Question 3. The determinant of [2 -x -1, 2 -x 3x, 1 -1 2x] is _____?

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A. -3x² + 5x + 2

B. X² -5x +20

C. 7x² + 5x +2

D. X² – 5x + 2

Answer is A. -3x² + 5x + 2

Question 4. Question 3. The determinant of [x 2 1, x 5 2x, 3 x 4] is _____?

A. 11

B. X² – 4x + 5

C. X – 2x

D. -2x³ + x² + 24x + 15

Answer D. -2x³ + x² + 24x + 15

Question 5. Every vector space is isomorphic to its____dual?

A. Ist

B. 2nd

C. 3rd

D. 4th

Answer is B. 2nd

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Question 6. For any linear transformation T:U->V let the dimension of U be finite, then ker T has_____ dimension?

A. Finite

B. Infinite

C. Linear

D. Non linear

Answer is A. Finite

Question 7. The dimension of the kernet of T is the same as the _____ of T?

A. Range

B. Rank

C. Nullity

D. Space

Answer is C. Nullity

Question 8. Question 4. Question 3. The determinant of [2 3 1, 0 0 0, 4 5 9] is _____?

A. 10

B. 4

C. Zero

D. 1

Answer is C. Zero

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Question 9. a matrix whose determinant is zero is called_____?

A. Symmetric

B. Non-symmetrical

C. Singular

D. Non singular

Answer is C. Singular

Question 10.

Question 7. The dimension of the kernet of T is the same as the _____ of T?

A. Range

B. Rank

C. Nullity

D. Space

Answer is C. Nullity

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