The value of x is such that matrix product - 2 0 7- 0 1 0- 1 -2 1 - -x 14x 7x- 0 1 0- x -4x -2x - equals an identity matrix- Then the value of 20x is

The correct option is A 4 [ 2 amp; 0 amp; 7; 0 amp; 1 amp; 0; 1 amp; 2 amp; 1 ] nbsp;[ x amp; 14x amp; 7x; 0 amp ...

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Multiplication of Matrices

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The value of x is such that matrix product $⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} - x & 14 x & 7 x 0 & 1 & 0 x & - 4 x & - 2 x \end{matrix} ⎤ ⎥ ⎦$ equals an identity matrix. Then the value of 20x is

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x

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦

B = ⎡ ⎢ ⎣ \begin{matrix} - x & 14 x & 7 x 0 & 1 & 0 x & - 4 x & - 2 x \end{matrix} ⎤ ⎥ ⎦

k,

10 k

⎛ ⎜ ⎝ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦ \times ⎛ ⎜ ⎝ \begin{matrix} - x & 14 x & 7 x 0 & 1 & 0 x & - 4 x & - 2 x \end{matrix} ⎤ ⎥ ⎦

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦

⎡ ⎢ ⎣ \begin{matrix} - α & 14 α & 7 α 0 & 1 & 0 α & - 4 α & - 2 α \end{matrix} ⎤ ⎥ ⎦

A B = I

I

3

B

[\begin{matrix} 2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & - 2 & 1 \end{matrix}] [\begin{matrix} - x & 14 x & 7 x \\ 0 & 1 & 0 \\ x & - 4 x & - 2 x \end{matrix}]

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦

B = ⎡ ⎢ ⎣ \begin{matrix} - x & 14 x & 7 x 0 & 1 & 0 x & - 4 x & - 2 x \end{matrix} ⎤ ⎥ ⎦

A B = (A B)^{- 1}

A B \neq I

I

3 \times 3

T r . (A B + (A B)^{2} + (A B)^{3} + . . . + (A B)^{100})

T r . (A)

A

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