If A = \( \begin{pmatrix}-1&2\\1&-4\end{pmatrix}\) then A (adj A) is:

1.	If A = \( \begin{pmatrix}-1&2\\1&-4\end{pmatrix}\) then A (adj A) is: (a) \( \begin{pmatrix}-4&-2\\-1&-1\end{pmatrix}\)(b) \( \begin{pmatrix}4&-2\\-1&1\end{pmatrix}\)(c) \( \begin{pmatrix}2&0\\0&2\end{pmatrix}\)(d) \( \begin{pmatrix}0&2\\2&0\end{pmatrix}\)
Answer» (c) \( \begin{pmatrix} 2&0\\0&2 \end{pmatrix}\) A = \( \begin{pmatrix} -1&2\\1&-4 \end{pmatrix}\) \|A\| = 4 – 2 = 2 We know that A (adj A) = \|A\| ⇒ 2\( \begin{pmatrix} 1&0\\0&1 \end{pmatrix}\) = \( \begin{pmatrix} 2&0\\0&2 \end{pmatrix}\)

If A = \( \begin{pmatrix}-1&2\\1&-4\end{pmatrix}\) then A (adj A) is: (a) \( \begin{pmatrix}-4&-2\\-1&-1\end{pmatrix}\)(b) \( \begin{pmatrix}4&-2\\-1&1\end{pmatrix}\)(c) \( \begin{pmatrix}2&0\\0&2\end{pmatrix}\)(d) \( \begin{pmatrix}0&2\\2&0\end{pmatrix}\)

Answer»

(c) \( \begin{pmatrix} 2&0\\0&2 \end{pmatrix}\)

A = \( \begin{pmatrix} -1&2\\1&-4 \end{pmatrix}\)

|A| = 4 – 2 = 2

We know that A (adj A) = |A|

⇒ 2\( \begin{pmatrix} 1&0\\0&1 \end{pmatrix}\) = \( \begin{pmatrix} 2&0\\0&2 \end{pmatrix}\)

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If A = \( \begin{pmatrix}-1&amp;2\\1&amp;-4\end{pmatrix}\) then A (adj A) is: (a) \( \begin{pmatrix}-4&amp;-2\\-1&amp;-1\end{pmatrix}\)(b) \( \begin{pmatrix}4&amp;-2\\-1&amp;1\end{pmatrix}\)(c) \( \begin{pmatrix}2&amp;0\\0&amp;2\end{pmatrix}\)(d) \( \begin{pmatrix}0&amp;2\\2&amp;0\end{pmatrix}\)

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If A = \( \begin{pmatrix}-1&2\\1&-4\end{pmatrix}\) then A (adj A) is: (a) \( \begin{pmatrix}-4&-2\\-1&-1\end{pmatrix}\)(b) \( \begin{pmatrix}4&-2\\-1&1\end{pmatrix}\)(c) \( \begin{pmatrix}2&0\\0&2\end{pmatrix}\)(d) \( \begin{pmatrix}0&2\\2&0\end{pmatrix}\)