Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 20248 AprilMorning Shift
Exam
JEE Main
Year
2024
Date
8 April
Shift
Morning Shift
Subject
Mathematics
Chapter
Matrices

JEE Main 2024 · 8 April · Morning Shift · Mathematics · Matrices

Let A=[ array lll 2 & a & 0 1 & 3 & 1 0 & 5 & b array ] . If A^3=4...

Let A=\left[2a013105b\begin{array}{lll}2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b\end{array}\right]. If A3=4A2−A−21IA^3=4 A^2-A-21 I, where II is the identity matrix of order 3×33 \times 3, then 2a+3b2 a+3 b is equal to

Options

  1. A-9
  2. B-13
  3. C-10
  4. D-12

Correct answer

B. -13

Step-by-step solution

A3−4A2+A+21I=0tr⁡(A)=4=5+6⇒b=−1∣A∣=−21−16+a=−21⇒a=−52a+3b=−13\begin{aligned} & A^3-4 A^2+A+21 I=0 \\ & \operatorname{tr}(A)=4=5+6 \Rightarrow b=-1 \\ & |A|=-21 \\ & -16+a=-21 \Rightarrow a=-5 \\ & 2 a+3 b=-13\end{aligned}
Practice Matrices on Quantrex Academy →

More from Matrices

Which one of the following matrices can be obtained by performing elementary row… JEE Advanced 2026Consider the matrix M = bmatrix 2 & -1 1 & 0 bmatrix . Let p, q, r, s, a, b, c and d be… JEE Advanced 2026For real numbers α, β, γ, δ and μ , consider the matrix M = bmatrix α & 1 2 & - 1 2 1 3 &… JEE Advanced 2026Let ℝ denote the set of all real numbers and let i = -1 . Consider the matrices S =… JEE Advanced 2026Let A = bmatrix α & 1 & 2 2 & 3 & 0 0 & 4 & 5 bmatrix and B = bmatrix 1 & 0 & 0 0 & -5α &… JEE Main 2026Let A = bmatrix 1 & 0 & 0 3 & 1 & 0 9 & 3 & 1 bmatrix and B = [b_ ij ] , 1 ≤ i, j ≤ 3 .… JEE Main 2026Let A = bmatrix -1 & 1 & -1 1 & 0 & 1 0 & 0 & 1 bmatrix satisfy A^2 + α(adj(adj(A))) +… JEE Main 2026Let M be a 3 × 3 matrix such that M pmatrix 1 0 0 pmatrix = pmatrix 1 2 3 pmatrix , M… JEE Main 2026Let A be a 3 × 3 matrix such that A^T bmatrix 1 0 1 bmatrix = bmatrix 5 2 2 bmatrix , A^T… JEE Main 2026Let A= bmatrix 1 & 2 & 7 4 & -2 & 8 3 & 8 & -7 bmatrix and (A-α I)=0 , where α is a real… JEE Main 2026Let S = \ A = bmatrix a & b c & d bmatrix : a, b, c, d ∈ \ 0, 1, 2, 3, 4\ and A^2 - 4A +… JEE Main 2026Let A = bmatrix 1 & 1 & 2 -2 & 0 & 1 1 & 3 & 5 bmatrix . Then the sum of all elements of… JEE Main 2026Consider the matrices A = bmatrix 2 & -2 4 & -2 bmatrix and B = bmatrix 3 & 9 1 & 3… JEE Main 2026Let A = bmatrix 1 & 2 1 & α bmatrix and B = bmatrix 3 & 3 β & 2 bmatrix . If A^2 - 4A + I… JEE Main 2026Let A=[ array ll 3 & -4 1 & -1 array ] and B be two matrices such that A^ 100 =100 B+I .… JEE Main 2026Let A, B and C be three 2 × 2 matrices with real entries such that B=(I+A)^ -1 and A+C=I… JEE Main 2026 Full Matrices list Matrices JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs