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Multiplication of Matrices

Find the valu...

Question

Find the value of x for which the product of the follwing matrices equals an identity matrix.
$⎛ ⎜ ⎝ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦ \times ⎛ ⎜ ⎝ \begin{matrix} - x & 14 x & 7 x 0 & 1 & 0 x & - 4 x & - 2 x \end{matrix} ⎤ ⎥ ⎦$

\frac{1}{5}

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\frac{1}{4}

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\frac{2}{3}

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\frac{1}{2}

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Solution

The correct option is A $\frac{1}{5}$
$⎛ ⎜ ⎝ \begin{matrix} 2 & 0 & 7 0 & 1 & 0 1 & - 2 & 1 \end{matrix} ⎤ ⎥ ⎦ \times ⎛ ⎜ ⎝ \begin{matrix} - x & 14 x & 7 x 0 & 1 & 0 x & - 4 x & - 2 x \end{matrix} ⎤ ⎥ ⎦ = ⎛ ⎜ ⎝ \begin{matrix} 5 x & 0 & 0 0 & 1 & 0 0 & 10 x - 2 & 5 x \end{matrix} ⎤ ⎥ ⎦ = ⎛ ⎜ ⎝ \begin{matrix} 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ (given) \Rightarrow 5 x = 1 and 10 x - 2 = 0, \Rightarrow x = \frac{1}{5}$

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Similar questions

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

[\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}]

⎡ ⎢ ⎣ \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} ⎤ ⎥ ⎦

(\begin{matrix} cos α & sin α cos α & sin α \end{matrix})

(\begin{matrix} cos α & cos α sin α & sin α \end{matrix})

A B \neq I

Find the value of x for which the value of the expressions $2x + 2$ and $\frac{2}{5} (x + 7)$ are equal.

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