JEE Main 2026 — Mathematics Algebra

Let $M$M be the matrix whose columns are the given vectors. We have:

$$M = \begin{pmatrix} 1 & 0 & -1 \\ 2 & 1 & 1 \\ 3 & 2 & 1 \end{pmatrix}$$M=​123​012​−111​​

Given $M \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 \\ 7 \\ 11 \end{pmatrix}$M​xyz​​=​1711​​, we can write this as a system of linear equations:

$$x - z = 1$$x−z=1

$$2x + y + z = 7$$2x+y+z=7

$$3x + 2y + z = 11$$3x+2y+z=11

Subtracting the second equation from the third equation gives:

$$x + y = 4$$x+y=4

Adding the first equation and the second equation gives:

$$3x + y = 8$$3x+y=8

Subtracting the equation $x + y = 4$x+y=4 from $3x + y = 8$3x+y=8 gives:

$$2x = 4 \Rightarrow x = 2$$2x=4⇒x=2

Substituting $x = 2$x=2 into $x + y = 4$x+y=4 gives:

$$2 + y = 4 \Rightarrow y = 2$$2+y=4⇒y=2

Substituting $x = 2$x=2 into $x - z = 1$x−z=1 gives:

$$2 - z = 1 \Rightarrow z = 1$$2−z=1⇒z=1

Therefore, $x + y + z = 2 + 2 + 1 = 5$x+y+z=2+2+1=5.

Answer: $5$5