Matrices
NCERT Class 12
CBSE
Grade 12
Question:
Find values of $x$ such that $\begin{bmatrix} 1 & x & 1 \end{bmatrix} \begin{bmatrix} 1 & 3 & 2 \\ 2 & 5 & 1 \\ 15 & 3 & 2 \end{bmatrix} \begin{bmatrix} 1 \\ 2 \\ x \end{bmatrix} = O$.
Step-by-Step Solution
First product: $\begin{bmatrix} 2x+16 & 5x+6 & x+4 \end{bmatrix}$. [1.0 Mark]
$(2x+16) + (10x+12) + (x^2+4x) = 0 \Rightarrow x^2 + 16x + 28 = 0$. [1.0 Mark]
$(x+14)(x+2) = 0 \Rightarrow x = -2$ or $x = -14$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating first row matrix product: 1.0 Mark
Forming quadratic equation $x^2 + 16x + 28 = 0$: 1.0 Mark
Solving roots $x = -2, -14$: 1.0 Mark
Correct Answer:
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