CUET UG 2025 — Mathematics Algebra

The given matrix equation is:

$$\begin{bmatrix} 1 & 2 & 1\end{bmatrix} \begin{bmatrix}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{bmatrix} \begin{bmatrix} 0 \\ 2 \\ x\end{bmatrix} = 0$$[1​2​1​]​121​200​012​​​02x​​=0

Multiply the first two matrices from left to right.

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$$\begin{bmatrix} 1 & 2 & 1\end{bmatrix} \times \begin{bmatrix}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{bmatrix}$$[1​2​1​]×​121​200​012​​

First element: $(1 \times 1) + (2 \times 2) + (1 \times 1)$(1×1)+(2×2)+(1×1)

$$= 1 + 4 + 1$$=1+4+1

$$= 6$$=6

Second element: $(1 \times 2) + (2 \times 0) + (1 \times 0)$(1×2)+(2×0)+(1×0)

$$= 2 + 0 + 0$$=2+0+0

$$= 2$$=2

Third element: $(1 \times 0) + (2 \times 1) + (1 \times 2)$(1×0)+(2×1)+(1×2)

$$= 0 + 2 + 2$$=0+2+2

$$= 4$$=4

Result: $$\begin{bmatrix} 6 & 2 & 4\end{bmatrix}$$[6​2​4​]

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$$\begin{bmatrix} 6 & 2 & 4\end{bmatrix} \times \begin{bmatrix} 0 \\ 2 \\ x\end{bmatrix} = 0$$[6​2​4​]×​02x​​=0

$$(6 \times 0) + (2 \times 2) + (4 \times x) = 0$$(6×0)+(2×2)+(4×x)=0

$$0 + 4 + 4x = 0$$0+4+4x=0

$$4 + 4x = 0$$4+4x=0

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$$4x = -4$$4x=−4

$$x = \dfrac{-4}{4}$$x=4−4​

$$x = -1$$x=−1

Therefore, the value of $x = -1$x=−1.