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CBSE Class 12 Math 2018 Solved Paper

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Question : 2 of 29
Marks: +1, -0
If the matrix A = (0a−320−1b10)\begin{pmatrix} 0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0 \end{pmatrix} is skew symmetric, find the values of 'a' and 'b'
Solution:  
Given that A = (0a−320−1b10)\begin{pmatrix} 0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0 \end{pmatrix} is skew symmetric matrix
⇒ ATA^T = - A
⇒ [0a−320−1b10]T\begin{bmatrix} 0 & a & -3 \\ 2 & 0 & -1 \\ b & 1 & 0 \end{bmatrix}^T = - [02ba01−3−10]\begin{bmatrix} 0 & 2 & b \\ a & 0 & 1 \\ -3 & -1 & 0 \end{bmatrix}
⇒ [02ba01−3−10]\begin{bmatrix} 0 & 2 & b \\ a & 0 & 1 \\ -3 & -1 & 0 \end{bmatrix} = [0−a3−201−b−10]\begin{bmatrix} 0 & -a & 3 \\ -2 & 0 & 1 \\ -b & -1 & 0 \end{bmatrix}
∴ By equality of Matrices,
a = - 2 and b = 3
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