Home
Class 12
MATHS
If the rank of the matrix [[-1,2,5],[2,-...

If the rank of the matrix `[[-1,2,5],[2,-4,a-4],[1,-2,a+1]]` is `1` then the value of `a` is (A) `-1` (B) 2 (C) `-6` (D) 4

A

`2, if a=-6`

B

`2, if a=1`

C

`1, if a=2`

D

`1, if a=-6`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Let `A= [[-1, 2, 5],[2, -4, a-4],[1, -2, a+1]]`
Applying `R_(2) rarr R_(2) 2 R_(1) and R_(3) rarr R_(3) + R_(1)`, then
`A = [[-1, 2, 5],[0,0,a+6],[0,0,a+6]]`
Applying `R_(3) rarr R_(3) - R_(2)`, then
`A = [[-1, 2, 5],[0,0,a+6],[0,0,0]]`
For `a = - 6 , p (A) = 1`
For `a = 1,2,p (A) = 2`
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|16 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Single Integer Answer Type Questions)|10 Videos

  • MATRICES

    ARIHANT MATHS|Exercise Exercise (Single Option Correct Type Questions)|30 Videos

  • MATHEMATICAL INDUCTION

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|31 Videos

Similar Questions

Explore conceptually related problems

The rank of the matrix [[-1,2,5],[2,-4,a-4],[1,-2,a+1]] is (where a = - 6)

Find the rank of [(3,-1,2),(-3,1,2),(-6,2,4)]

For the matrix ( A=[[-3,6,0],[4,-5,8],[0,-7,-2]] ), find ( 1/2(A-A') ), where A' is the transpose of matrix A.

Express the matrix [[5,1,-1],[2,-3,4],[7,1,-3]] as a sum of symmetric and skew symmetric matrix

The number of values of x for which the matrix A=[(3-x,2,2),(2,4-x,1),(-2,-4,-1-x)] is singular, is

Consider three matrices A=[(2,1),(4,1)], B=[(3,4),(2,3)] and C=[(3,-4),(-2,3)]. Then the value of the sum tr(A)+tr((ABC)/2) +tr((A(BC)^2)/4)+tr((A(BC)^3)/8)+.......+oo is (A) 6 (B) 9 (C) 12 (D) none of these

If A = [[1,2,-3],[5,0,2],[1,-1,1]], B = [[3,-1,2],[4,2,5],[2,0,3]] and C = [[4,1,2],[0,3,2],[1,-2,3]] , then compute (A+B) and (B-C) . Also, verify that A + (B-C) = (A + B) - C .

There are two possible values of A in the solution of the matrix equation [[2A+1,-5],[-4,A]]^(-1) [[A-5,B],[2A-2,C]]= [[14,D],[E,F]] , where A, B, C, D, E, F are real numbers. The absolute value of the difference of these two solutions, is