CUET UG 2025 — Mathematics Algebra

The first matrix is a diagonal matrix, which simplifies the multiplication.

When multiplying the matrices, each row of the first matrix multiplies with the column of the second matrix.

First row calculation:

$$(1)(2x) + (0)(-2) + (0)(z-3)$$(1)(2x)+(0)(−2)+(0)(z−3)

$$= 2x$$=2x

Second row calculation:

$$(0)(2x) + (y+1)(-2) + (0)(z-3)$$(0)(2x)+(y+1)(−2)+(0)(z−3)

$$= -2(y+1)$$=−2(y+1)

$$= -2y - 2$$=−2y−2

Third row calculation:

$$(0)(2x) + (0)(-2) + (1)(z-3)$$(0)(2x)+(0)(−2)+(1)(z−3)

$$= z - 3$$=z−3

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After multiplication:

$$\begin{bmatrix} 2x \\ -2y-2 \\ z-3 \end{bmatrix} = \begin{bmatrix} 6 \\ 4 \\ 1 \end{bmatrix}$$​2x−2y−2z−3​​=​641​​

This gives three equations:

$$2x = 6$$2x=6

$$-2y - 2 = 4$$−2y−2=4

$$z - 3 = 1$$z−3=1

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For $x$x:

$$2x = 6$$2x=6

$$x = 3$$x=3

For $y$y:

$$-2y - 2 = 4$$−2y−2=4

$$-2y = 6$$−2y=6

$$y = -3$$y=−3

For $z$z:

$$z - 3 = 1$$z−3=1

$$z = 4$$z=4

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Therefore:

$$x + y + z$$x+y+z

$$= 3 + (-3) + 4$$=3+(−3)+4

$$= 4$$=4