InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
Which of the following is not the property of transpose of a matrix?(a) (A’)’=A(b) (A+B)’=A’+B’(c) (AB)’=(BA)’(d) (kA)’=KA’This question was posed to me by my college professor while I was bunking the class.I need to ask this question from Transpose of a Matrix topic in chapter Matrices of Mathematics – Class 12 |
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Answer» RIGHT option is (c) (AB)’=(BA)’ To elaborate: (AB)’=(BA)’is INCORRECT. We KNOW that matrix multiplication is not commutative i.e. AB≠BA. Hence, its transpose will ALSO not be commutative. (AB)’=B’A’ |
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| 52. |
State whether the given statement is true or false.The matrix A = \begin{bmatrix}0&0\\0&0\end{bmatrix}(a) True(b) FalseThe question was asked in an online interview.My question is taken from Types of Matrices in portion Matrices of Mathematics – Class 12 |
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Answer» RIGHT OPTION is (a) True Easiest explanation: The given statement is true. A MATRIX is CALLED a null or zero matrix if the value of all the elements in the matrix is 0. Thus A = \(\begin{bmatrix}0&0\\0&0\end{bmatrix}\). |
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| 53. |
Which of the following is the reversal law of transposes?(a) (A-B)’=B’-A’(b) (AB)’=B’A’(c) (AB)’=(BA)’(d) (A+B)’=B’+A’I had been asked this question during an online exam.I'd like to ask this question from Transpose of a Matrix topic in portion Matrices of Mathematics – Class 12 |
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Answer» CORRECT choice is (b) (AB)’=B’A’ For EXPLANATION: According to the REVERSE law of transposes the TRANSPOSE of the product is the product of the transposes TAKEN in the reverse order i.e. (AB)’=B’ A’. |
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| 54. |
The matrix which follows the condition m>n is called as ____________(a) vertical matrix(b) horizontal matrix(c) diagonal matrix(d) square matrixThe question was posed to me during an online interview.My question is taken from Types of Matrices in chapter Matrices of Mathematics – Class 12 |
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Answer» RIGHT choice is (a) vertical matrix Explanation: The matrix in which the NUMBER of COLUMNS is GREATER than the number of rows is called a vertical matrix. There the matrix which follows the condition m>n is a vertical matrix. |
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| 55. |
Find the value of a,b,c,d if \(\begin{bmatrix}a+b&c\\a-b&2c+d\end{bmatrix}\)=\(\begin{bmatrix}3&2\\1&6\end{bmatrix}\).(a) 3, 2, 1, 4(b) 3, 2, 1, 6(c) 2, 2, 2, 2(d) 2, 1, 2, 2The question was asked during an interview for a job.Origin of the question is Types of Matrices in section Matrices of Mathematics – Class 12 |
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Answer» The correct choice is (d) 2, 1, 2, 2 |
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| 56. |
The addition of matrices is only possible if they are of the same order.(a) True(b) FalseThis question was addressed to me during an interview.I would like to ask this question from Operations on Matrices in division Matrices of Mathematics – Class 12 |
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Answer» The correct choice is (a) True |
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| 57. |
Which of the following matrices will not have an inverse?(a) \(\begin{bmatrix}2&4\\-1&1\end{bmatrix}\)(b) \(\begin{bmatrix}1&5&2\\6&4&2\\1&3&2\end{bmatrix}\)(c) \(\begin{bmatrix}1&2\\1&1\end{bmatrix}\)(d) \(\begin{bmatrix}1&2&5\\3&6&4\end{bmatrix}\)This question was posed to me in class test.Enquiry is from Invertible Matrices topic in portion Matrices of Mathematics – Class 12 |
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Answer» CORRECT option is (d) \(\begin{BMATRIX}1&2&5\\3&6&4\end{bmatrix}\) The explanation: The matrix A=\(\begin{bmatrix}1&2&5\\3&6&4\end{bmatrix}\) will not have an inverse as it is a rectangular matrix. Rectangular matrix does not possess an inverse matrix. |
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| 58. |
How many elementary operations are possible on Matrices?(a) 3(b) 2(c) 6(d) 5This question was posed to me in an interview.I'm obligated to ask this question of Elementary Operation (Transformation) of a Matrix topic in division Matrices of Mathematics – Class 12 |
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Answer» Correct answer is (C) 6 |
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