Linear Algebra

1. [A] is square matrix which is neither symmetric nor skew-symmetric and [A]T is its transpose. The sum and difference of these matrices are defined as [S] = [A] + [A]T and [D] = [A] – [A]T, respectively. Which of the following statements is TRUE? A. Both [S] and [D] are symmetric B. Both [S] and [D] are skew-symmetric C. [S] is skew-symmetric and [D] is symmetric D. [S] is symmetric and [D] is skew-symmetric

”Both
and [D] are symmetric” option2=”Both [S] and [D] are skew-symmetric” option3=”[S] is skew-symmetric and [D] is symmetric” option4=”[S] is symmetric and [D] is skew-symmetric” correct=”option1″]

Detailed Solution[A] is square matrix which is neither symmetric nor skew-symmetric and [A]T is its transpose. The sum and difference of these matrices are defined as [S] = [A] + [A]T and [D] = [A] – [A]T, respectively. Which of the following statements is TRUE? A. Both [S] and [D] are symmetric B. Both [S] and [D] are skew-symmetric C.

Join Our Telegram Channel
Subscribe on YouTube
[S] is skew-symmetric and [D] is symmetric D. [S] is symmetric and [D] is skew-symmetric

2. Consider the matrix as given below: \[\left[ {\begin{array}{*{20}{c}} 1&2&3 \\ 0&4&7 \\ 0&0&3 \end{array}} \right]\] Which one of the following options provides the CORRECT values of the eigen values of the matrix? A. 1, 4. 3 B. 3, 7, 3 C. 7, 3, 2 D. 1, 2, 3

1, 4. 3
3, 7, 3
7, 3, 2
1, 2, 3

Subscribe on YouTube

of the eigen values of the matrix? A. 1, 4. 3 B. 3, 7, 3 C. 7, 3,
Join Our Telegram Channel
2 D. 1, 2, 3" class="read-more button" href="https://exam.pscnotes.com/mcq/consider-the-matrix-as-given-below-left-beginarray20c-123-047-003-endarray-right-which-one-of-the-following-options-provides-the-correct-values-of-the-eig/#more-20016">Detailed SolutionConsider the matrix as given below: \[\left[ {\begin{array}{*{20}{c}} 1&2&3 \\ 0&4&7 \\ 0&0&3 \end{array}} \right]\] Which one of the following options provides the CORRECT values of the eigen values of the matrix? A. 1, 4. 3 B. 3, 7, 3 C. 7, 3, 2 D. 1, 2, 3

3. Consider the following system of linear equations: 3x + 2ky = -2 kx + 6y = 2 Here, x and y are the unknown and k is a real constant. The value of k for which there are infinite number of solutions is A. 3 B. 1 C. -3 D. -6

3
1
-3
-6

Detailed SolutionConsider the following system of linear equations: 3x + 2ky = -2 kx + 6y = 2

Join Our Telegram Channel
Subscribe on YouTube
Here, x and y are the unknown and k is a real constant. The value of k for which there are infinite number of solutions is A. 3 B. 1 C. -3 D. -6

4. Given Matrix \[\left[ {\text{A}} \right] = \left[ {\begin{array}{*{20}{c}} 4&2&1&3 \\ 6&3&4&7 \\ 2&1&0&1 \end{array}} \right],\] the rank of the matrix is A. 4 B. 3 C. 2 D. 1

4
3
2
1

Subscribe on YouTube

Join Our Telegram Channel
class="read-more button" href="https://exam.pscnotes.com/mcq/given-matrix-left-texta-right-left-beginarray20c-4213-6347-2101-endarray-right-the-rank-of-the-matrix-is-a-4-b-3-c-2-d-1/#more-20014">Detailed SolutionGiven Matrix \[\left[ {\text{A}} \right] = \left[ {\begin{array}{*{20}{c}} 4&2&1&3 \\ 6&3&4&7 \\ 2&1&0&1 \end{array}} \right],\] the rank of the matrix is A. 4 B. 3 C. 2 D. 1

5. The number of solutions of the simultaneous algebraic equation y = 3x + 3 and y = 3x + 5 is: A. zero B. 1 C. 2 D. Infinite

zero
1
2
Infinite

Join Our Telegram Channel
Subscribe on YouTube
1 C. 2 D. Infinite" class="read-more button" href="https://exam.pscnotes.com/mcq/the-number-of-solutions-of-the-simultaneous-algebraic-equation-y-3x-3-and-y-3x-5-is-a-zero-b-1-c-2-d-infinite/#more-20013">Detailed SolutionThe number of solutions of the simultaneous algebraic equation y = 3x + 3 and y = 3x + 5 is: A. zero B. 1 C. 2 D. Infinite

6. For which value of x will the matrix given below become singular? \[\left[ {\begin{array}{*{20}{c}} 8&{\text{x}}&0 \\ 4&0&2 \\ {12}&6&0 \end{array}} \right]\] A. 4 B. 6 C. 8 D. 12

4
6
8
12

Detailed SolutionFor which value of x will the matrix given below become singular? \[\left[ {\begin{array}{*{20}{c}} 8&{\text{x}}&0 \\

Join Our Telegram Channel
Subscribe on YouTube
4&0&2 \\ {12}&6&0 \end{array}} \right]\] A. 4 B. 6 C. 8 D. 12

7. Consider the following linear system. x + 2y – 3z = a 2x + 3y + 3z = b 5x + 9y – 6z = c This system is consistent if a, b and c satisfy the equation A. 7a – b – c = 0 B. 3a + b – c = 0 C. 3a – b + c = 0 D. 7a – b + c = 0

7a - b - c = 0
3a + b - c = 0
3a - b + c = 0

Detailed SolutionConsider the following linear system. x + 2y – 3z = a 2x + 3y + 3z = b 5x + 9y – 6z = c This system is consistent if a, b and c satisfy the equation A. 7a – b – c = 0 B. 3a + b – c = 0 C. 3a – b + c = 0 D. 7a – b + c = 0

8. The rank of the matrix \[\left[ {\begin{array}{*{20}{c}} { – 4}&1&{ – 1} \\ { – 1}&{ – 1}&{ – 1} \\ 7&{ – 3}&1 \end{array}} \right]\] is A. 1 B. 2 C. 3 D. 4

1
2
3
4

Join Our Telegram Channel
Subscribe on YouTube
2 C. 3 D. 4" class="read-more button" href="https://exam.pscnotes.com/mcq/the-rank-of-the-matrix-left-beginarray20c-41-1-1-1-1-7-31-endarray-right-is-a-1-b-2-c-3-d-4/#more-20010">Detailed SolutionThe rank of the matrix \[\left[ {\begin{array}{*{20}{c}} { – 4}&1&{ – 1} \\ { – 1}&{ – 1}&{ – 1} \\ 7&{ – 3}&1 \end{array}} \right]\] is A. 1 B. 2 C. 3 D. 4

9. Consider the matrices X(4 × 3), Y(4 × 3) and P(2 × 3). The order of [P(XTY)-1 PT]T will be A. (2 × 2) B. (3 × 3) C. (4 × 3) D. (3 × 4)

(2 × 2)
(3 × 3)
(4 × 3)
(3 × 4)

Join Our Telegram Channel

64 288 64S117.2 64 74.6 75.5c-23.5 6.3-42 24.9-48.3 48.6-11.4 42.9-11.4 132.3-11.4 132.3s0 89.4 11.4 132.3c6.3 23.7 24.8 41.5 48.3 47.8C117.2 448 288 448 288 448s170.8 0 213.4-11.5c23.5-6.3 42-24.2 48.3-47.8 11.4-42.9 11.4-132.3 11.4-132.3s0-89.4-11.4-132.3zm-317.5 213.5V175.2l142.7 81.2-142.7 81.2z"/> Subscribe on YouTube C. (4 × 3) D. (3 × 4)" class="read-more button" href="https://exam.pscnotes.com/mcq/consider-the-matrices-x4-a%c2%97-3-y4-a%c2%97-3-and-p2-a%c2%97-3-the-order-of-pxty-1-ptt-will-be-a-2-a%c2%97-2-b-3-a%c2%97-3-c-4-a%c2%97-3-d-3-a%c2%97-4/#more-20009">Detailed SolutionConsider the matrices X(4 × 3), Y(4 × 3) and P(2 × 3). The order of [P(XTY)-1 PT]T will be A. (2 × 2) B. (3 × 3) C. (4 × 3) D. (3 × 4)

10. A square matrix B is skew-symmetric if A. BT = -B B. BT = B C. B-1 = B D. B-1 = BT

BT = -B
BT = B
B-1 = B
B-1 = BT

Join Our Telegram Channel
Subscribe on YouTube
A. BT = -B B. BT = B C. B-1 = B D. B-1 = BT" class="read-more button" href="https://exam.pscnotes.com/mcq/a-square-matrix-b-is-skew-symmetric-if-a-bt-b-b-bt-b-c-b-1-b-d-b-1-bt/#more-20008">Detailed SolutionA square matrix B is skew-symmetric if A. BT = -B B. BT = B C. B-1 = B D. B-1 = BT

Page 1Page 2Page 3Page 4Page 5
Test 1Test 2Test 3