COMPASSLearning

Talk to us Register Login

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Matrices

Let M be a

3 \times 3

matrix such that

M 100 = 123, M 010 = 012

and

M 001 = - 1 11

. If

M x y z = 1711

, then

x + y + z

equals :

(A)4
(B)5✓ Correct
(C)7
(D)11

Answer: (B)

Solution

The images of the standard basis vectors are the columns of

M

, so

M = 123012 - 1 11

. The system

M (x, y, z)^{T} = (1, 7, 11)^{T}

reads

x - z = 1

,

2 x + y + z = 7

,

3 x + 2 y + z = 11

. From the first,

z = x - 1

; substitution gives

3 x + y = 8

and

2 x + y = 6

, whence

x = 2, y = 2, z = 1

. Therefore

x + y + z = 5

.

JEE Main · 2026 · 05 Apr 2026 · Shift 2 · Single correct option

Practise more: all JEE Main PYQs on Matrices →

More JEE Main questions on Matrices

For some $α, β \in R$ , let $A = [α 1 22]$ and $B = [11 1 β]$ be such that $A^{2} - 4 A + 2 I = B^{2} - 3 B + I = O$ . Then …
JEE Main 2026View solution →
For the matrices $A = [31 - 4 - 1]$ and $B = [- 29 - 13 4918]$ , if …
JEE Main 2026View solution →
If the system of equations
$3 x + y + 4 z = 3$
$2 x + α y - z = - 3$
$x + 2 y + z = 4$
has no solution, then the value of $α$ is equal to:
JEE Main 2026View solution →
If $A = [2335]$ , then the determinant of the matrix $(A^{2025} - 3 A^{2024} + A^{2023})$ is
JEE Main 2026View solution →
Let A be a $3 \times 3$ matrix such that $A + A^{T} = O$ . If …
JEE Main 2026View solution →
If $X = x y z$ is a solution of the system of equations $A X = B$ , where $adj A = 4 - 5 1 20 - 2 253$ and $B = 402$ , then $∣ x + y + z ∣$ is equal t …
JEE Main 2026View solution →