Find the value of x, if

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

Find the value of x, if $[\begin{array}{lll} 1 x 1 \end{array}] [\begin{array}{ccc} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{array}] [\begin{array}{l} 1 \\ 2 \\ x \end{array}] = O .$

– 2

– 14

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Given, ${[\begin{array}{lll} 1 x 1 \end{array}]}_{1 \times 3} {[\begin{array}{ccc} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{array}]}_{3 \times 3} {[\begin{array}{l} 1 \\ 2 \\ x \end{array}]}_{3 \times 1} = O$
$\Rightarrow [\begin{array}{lll} 1 + 2 x + 15 3 + 5 x + 3 2 + x + 2 \end{array}] [\begin{array}{l} 1 \\ 2 \\ x \end{array}] = O$

$\Rightarrow [16 + 2 x + 153 + 5 x + 32 + x + 2] [\begin{array}{l} 1 \\ 2 \\ x \end{array}] = O$
⇒ [(16 + 2x) ⋅ 1 + (6 + 5x) ⋅ 2 + (4 + x) ⋅ x] = 0

⇒ (16 + 2x) + (12 + 10x) + (4x + x²) = 0

⇒ x² + 16x + 28 = 0 ⇒ (x + 14) (x + 2) = 0

⇒ x + 14 = 0 or x + 2 = 0

Hence, x = – 14 or x = – 2.

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