Matrix

Study Material (PDF)
Self Assesment
Study Material (PDF)
Self Assesment

Click on each question to see answer & solution.

Question No: #1

If `A = [a_{ij}]` is a matrix of order `2\times\2` where `a_{ij} = i+2j` then find the matrix `A`.
Ans: $ A= \begin{bmatrix} 3 & 5 \\ 4 & 6 \end{bmatrix} $
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Question No: #2

If `A = [a_{ij}]` is a matrix of order `2\times\2` where `a_{ij} = \frac{(i+j)^2}{2}`, then find the matrix `A`.
Ans: $ \begin{pmatrix} 2 & 9/2 \\ 9/2 & 8 \end{pmatrix} $
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Question No: #3

If `A = (a_{ij})_{n\times\n}` is a square matrix where `a_{ij} = i^2-j^2`, then matrix `A` is -- (a) zero matrix, (b) unit matrix, (c) symmetric matrix, (d) skew-symmetric matrix
Ans: (d) skew-symmetric matrix
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Question No: #4

If $ A = \begin{pmatrix} 3x & x-1 \\ 2x+3 & x+2 \end{pmatrix} $ is a symmetric matrix, then find the value of `x`.
Ans: `-4`
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Question No: #5

If $ A = \begin{bmatrix} 0 & x & 7 \\ -2 & z & 3 \\ y & w & 0 \end{bmatrix} $ is a skew-symmetric matrix,then find the value of `x, y, z`
Ans: `x=2, y=-7, z=0`
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Question No: #6

Show that `A-A^T` is a skew-symmetric matrix where $A=\begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix}$
Ans: N.A.
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Question No: #7

If $ A = \begin{pmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{pmatrix} $ then show that `A+A^T` is a symmetric matrix.
Ans: N.A.
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Question No: #8

If $ A = \begin{bmatrix} -i & 0 \\ 0 & i \end{bmatrix} $ then `A^TA` is equal to - (a) `A` (b) `-A` (c) `I` (d) `-I`
Ans: (d) `-I`
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Question No: #9

If `A` is a square matrix, then `A\A^T + A^TA` is -- (a) unit matrix (b) zero matrix (c) symmetric matrix (d) skew-symmetric matrix
Ans: (c) symmetric matrix
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Question No: #10

If `A` be a square matrix, then which of the following is false: (a) `(A^T)^T = A`, (b) `A+A^T` is symmetric, (c) `A-A^T` is skew-symmetric, (d) `(AB)^T = B^T\cdotA^T`
Ans: All options are correct
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