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Consider a matrix A = \(\begin{bmatrix}-1&1&1\\1&-1&1\\1&1&-1\end{bmatrix}\). If |2 adj(3 adj(4A-1))| = 2a.3b, then the value of a - 2b is |
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Answer» A = \(\begin{bmatrix}-1&1&1\\1&-1&1\\1&1&-1\end{bmatrix}\) |A| = -1 + 1 + 1 + 1 + 1 + 1 = 4 Now, |2 adj (3adj(4A-1))| = 23|adj(3adj (4A-1))| (\(\because\) |KA| = Kn|A|) = 23|3adj(4A-1)|2 (\(\because\) |adj A| = |A|n-1) = 23(33|adj (4A-1)|)2 (\(\because\) |KA| = Kn|A|) = 23.36 |adj(4A-1)|4 = 23.36(43. (A-1))4 (\(\because\) |KA| = Kn|A|) = 23.36(43. \(\frac14\)) (\(\because\) |A-1| = \(\frac1{|A|}=\frac14\)) = 23.36(42)4 = 23.36.48 = 23.36.216 = 219.36 \(\therefore\) a = 19, b = 6 \(\therefore\) a - 2b = 19 - 12 = 7 |
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