JEE Main 2026 Jan 22 Shift 2, Mathematics Q9: System Of Linear Equations

JEE Main2026Jan 22, Shift 2Mathematics

If $X = x y z$ is a solution of the system of equations $A X = B$ , where $adj A = 422 - 505 1 - 23$ and $B = 402$ , then $∣ x + y + z ∣$ is equal to :

A
3
B
$\frac{3}{2}$
C
1
D
2

Solution

For a $3 \times 3$ matrix, $∣ adj A ∣ = ∣ A ∣^{2}$ .

$∣ adj A ∣ = 4 (0 + 10) - 2 (- 15 - 5) + 2 (10 - 0) = 40 + 40 + 20 = 100$ , so $∣ A ∣ = \pm 10$ .

$X = A^{- 1} B = \frac{adj A}{∣ A ∣} B = \pm \frac{1}{10} 422 - 505 1 - 23 402 = \pm \frac{1}{10} 20 - 10 10 = \pm 2 - 1 1$ .

$∣ x + y + z ∣ = ∣2 - 1 + 1∣ = 2$ .

Concept behind this question

System Of Linear EquationsNotes, formulas and examples →

Practice more Mathematics

Concept-wise practice with instant solutions on Fundamenthol.

Start practicing →

JEE Main 2026 Jan 22 Shift 2, Mathematics Q9: System Of Linear Equations

Concept behind this question

More previous year questions on System Of Linear Equations

Practice more Mathematics