COMPASSLearning

Talk to us Register Login

JEE Main · 2025 · 29 Jan 2025 · Shift 2 · Matrices

Let

A = [a_{ij}]

be a matrix of order

3 \times 3

, with

a_{ij} = (2)^{i + j}

. If the sum of all the elements in the third row of

A^{2}

is

α + β 2, α, β \in Z

, then

α + β

is equal to

(A)280
(B)168
(C)210
(D)224✓ Correct

Answer: (D)

Solution

With

a_{ij} = (2)^{i + j}

:

A = 2224224424428

The third row of

A^{2}

is (third row of

A

)

\times A

, i.e.

(4, 42, 8) \cdot A

:

col 1: 4 (2) + 42 (22) + 8 (4) = 8 + 16 + 32 = 56

col 2: 4 (22) + 42 (4) + 8 (42) = 82 + 162 + 322 = 562

col 3: 4 (4) + 42 (42) + 8 (8) = 16 + 32 + 64 = 112

Sum of the third row

= 56 + 562 + 112 = 168 + 562

, so

α = 168, β = 56

, and

α + β = 224

JEE Main · 2025 · 29 Jan 2025 · 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 →