Find the matrix A such that - - 2 - 1- 1 0- - 3 4 -A - - - - 1 - 8- 1 - 2- 9 22 -

[ [ [ 2 amp; 1; 1 amp;0; 3 amp;4 ]]A = [ [ 1 amp; 8; 1 amp; 2; ...

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Standard XII

Mathematics

Finding Inverse Using Elementary Transformations

Find the matr...

Question

Find the matrix $A$ such that $⎡ ⎢ ⎣ \begin{matrix} 2 & - 1 1 & 0 - 3 & 4 \end{matrix} ⎤ ⎥ ⎦ A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 8 1 & - 2 9 & 22 \end{matrix} ⎤ ⎥ ⎦$ .

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Solution

$\begin{matrix} ⎡ ⎢ ⎣ \begin{matrix} 2 & - 1 1 & 0 - 3 & 4 \end{matrix} ⎤ ⎥ ⎦ A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 8 1 & - 2 9 & 22 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} 2 & - 1 1 & 0 - 3 & 4 \end{matrix} ⎤ ⎥ ⎦ [\begin{matrix} a & b c & d \end{matrix}] = ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 8 1 & - 2 9 & 22 \end{matrix} ⎤ ⎥ ⎦ \Rightarrow ⎡ ⎢ ⎣ \begin{matrix} 2 a - c & 2 b - d a & b - 3 a + 4 c & - 3 b + 4 d \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 8 1 & - 2 9 & 22 \end{matrix} ⎤ ⎥ ⎦ a = 1, b = - 2 2 a - c = - 1 s o, c = 3 2 b - d = - 8 s o, d = 4 ∴ A = [\begin{matrix} 1 & - 2 3 & 4 \end{matrix}] \end{matrix}$

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⎡ ⎢ ⎣ \begin{matrix} 2 & - 1 1 & 0 - 3 & 4 \end{matrix} ⎤ ⎥ ⎦ A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 8 1 & - 2 9 & 22 \end{matrix} ⎤ ⎥ ⎦

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⎛ ⎜ ⎝ \begin{matrix} 2 & - 1 1 & 0 - 3 & 4 \end{matrix} ⎞ ⎟ ⎠ A = ⎛ ⎜ ⎝ \begin{matrix} - 1 & - 8 1 & - 2 9 & 22 \end{matrix} ⎞ ⎟ ⎠

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⎛ ⎜ ⎝ \begin{matrix} 2 & - 1 1 & 0 - 3 & 4 \end{matrix} ⎞ ⎟ ⎠ A = ⎛ ⎜ ⎝ \begin{matrix} - 1 & - 8 1 & - 2 9 & 22 \end{matrix} ⎞ ⎟ ⎠

Using properties of determinants,prove that $∣ ∣ ∣ ∣ \begin{matrix} a^{2} + 2 a & 2 a + 1 & 1 2 a + 1 & a + 2 & 1 3 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣ = (a - 1)^{3}$ .

OR find matrix A such that $⎛ ⎜ ⎝ \begin{matrix} 2 & - 1 1 & 0 - 3 & 4 \end{matrix} ⎞ ⎟ ⎠ A = ⎛ ⎜ ⎝ \begin{matrix} - 1 & - 8 1 & - 2 9 & 22 \end{matrix} ⎞ ⎟ ⎠ .$

⎡ ⎢ ⎣ \begin{matrix} 2 & 1 1 & 0 - 3 & 4 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} - 1 & - 8 1 & - 2 9 & 22 \end{matrix} ⎤ ⎥ ⎦

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Find the matrix A such that ⎡⎢⎣2−110−34⎤⎥⎦A=⎡⎢⎣−1−81−2922⎤⎥⎦.

⎡⎢⎣2−110−34⎤⎥⎦A=⎡⎢⎣−1−81−2922⎤⎥⎦⎡⎢⎣2−110−34⎤⎥⎦[abcd]=⎡⎢⎣−1−81−2922⎤⎥⎦⇒⎡⎢⎣2a−c2b−dab−3a+4c−3b+4d⎤⎥⎦=⎡⎢⎣−1−81−2922⎤⎥⎦a=1,b=−22a−c=−1so,c=32b−d=−8so,d=4∴A=[1−234]

Find the matrix $A$ such that $⎡ ⎢ ⎣ \begin{matrix} 2 & - 1 1 & 0 - 3 & 4 \end{matrix} ⎤ ⎥ ⎦ A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & - 8 1 & - 2 9 & 22 \end{matrix} ⎤ ⎥ ⎦$ .