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Properties of Matrix Multiplication

The value of ...

Question

The value of $x,$ if
$∣ ∣ ∣ \begin{matrix} 2 x & 5 8 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & 5 8 & 3 \end{matrix} ∣ ∣ ∣$ is

A

0

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B

1

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C

2

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D

- 3

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Solution

The correct option is D $- 3$
$∣ ∣ ∣ \begin{matrix} 2 x & 5 8 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & 5 8 & 3 \end{matrix} ∣ ∣ ∣$
$\Rightarrow 2 x \times x - 5 \times 8 = 6 \times 3 - 5 \times 8$
$\Rightarrow 2 x^{2} - 40 = 18 - 40$
$\Rightarrow 2 x^{2} = 18$
$\Rightarrow x^{2} = 9$
$\Rightarrow x = \pm 3$

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Similar questions

I f ∣ ∣ ∣ \begin{matrix} 2 x & 5 8 & x \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} 6 & - 2 7 & 3 \end{matrix} ∣ ∣ ∣, t h e n w r i t e t h e v a l u e o f | x | .

Q. Find the values of x, if

(i)

|\begin{matrix} 2 & 4 \\ 5 & 1 \end{matrix}| = |\begin{matrix} 2 x & 4 \\ 6 & x \end{matrix}|

|\begin{matrix} 2 & 3 \\ 4 & 5 \end{matrix}| = |\begin{matrix} x & 3 \\ 2 x & 5 \end{matrix}|

|\begin{matrix} 3 & x \\ x & 1 \end{matrix}| = |\begin{matrix} 3 & 2 \\ 4 & 1 \end{matrix}|

|\begin{matrix} 3 x & 7 \\ 2 & 4 \end{matrix}| = 10

, find the value of x.

(v)

|\begin{matrix} x + 1 & x - 1 \\ x - 3 & x + 2 \end{matrix}| = |\begin{matrix} 4 & - 1 \\ 1 & 3 \end{matrix}|

|\begin{matrix} 2 x & 5 \\ 8 & x \end{matrix}| = |\begin{matrix} 6 & 5 \\ 8 & 3 \end{matrix}|

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Properties of Matrix Multiplication

Standard X Mathematics

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