CUET CUET Mathematics 2024 - If the matrix [arrayrrr0 & -1 & 3 x \\ 1 & y & -5 \\ -6 & 5 & 0array] is skew-symmetric, then the value of 5 x-y is: | PYQs + Solutions | AfterBoards
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CUET Mathematics 2024

Algebra
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Matrices & Determinants

Medium

If the matrix [0−13x1y−5−650]\left[\begin{array}{rrr}0 & -1 & 3 x \\ 1 & y & -5 \\ -6 & 5 & 0\end{array}\right] is skew-symmetric, then the value of 5x−y5 x-y is:

Correct Option: 3
A=[0−13x1y−5−650]A = \left[\begin{array}{rrr}0 & -1 & 3x \\ 1 & y & -5 \\ -6 & 5 & 0\end{array}\right]
Applying the skew-symmetric property:
Diagonal elements must be zero: \newline y=0y = 0 (since the element at position (2,2)(2,2) must be zero)
Corresponding off-diagonal elements must be negatives of each other: \newline a13=3xa_{13} = 3x and a31=−6a_{31} = -6
Hence, \newline 3x=−(−6)3x = -(-6) \newline 3x=63x = 6 \newline x=2x = 2
∴5x−y=5(2)−0=10\therefore 5x-y = 5(2)-0 = 10

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