Home
Class 12
MATHS
Let psiA be defined as trace of a matrix...

Let `psi_A` be defined as trace of a matrix `A` which is sum of diagonal elements of a square matrix. `psi_(lambdaA+mu B) =`

A

(a) `lamdapsi_(A)+mupsi_(B)`

B

(b) `lamdapsi_(B)+mupsi_(A)`

C

(c) `lamdapsi_(AB)+mupsi_(BA)`

D

(d) none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MATRICES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - E) Assertion - Reason Type Questions|3 Videos
  • MATRICES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - F) Matrix - Match Type Question|1 Videos
  • MATRICES

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (Section - C) Objective Type Questions (More than one options are correct)|7 Videos
  • MATHEMATICAL REASONING

    AAKASH INSTITUTE ENGLISH|Exercise Assignment (SECTION-D) (Assertion-Reason Type Questions)|15 Videos
  • PERMUTATIONS AND COMBINATIONS

    AAKASH INSTITUTE ENGLISH|Exercise Assignment Section-J (Aakash Challengers Questions)|7 Videos

Similar Questions

Explore conceptually related problems

Let psi_A be defined as trace of a matrix A which is sum of diagonal elements of a square matrix. Which of the following is true?

If A is 2xx2 matrix such that A[{:(" "1),(-1):}]=[{:(-1),(2):}]and A^2[{:(" "1),(-1):}]=[{:(1),(0):}] , then trace of A is (where the trace of the matrix is the sum of all principal diagonal elements of the matrix )

If A=[(2, 1,-1),(3, 5,2),(1, 6, 1)] , then tr(Aadj(adjA)) is equal to (where, tr (P) denotes the trace of the matrix P i.e. the sum of all the diagonal elements of the matrix P and adj(P) denotes the adjoint of matrix P)

Consider the matrix A=[(x, 2y,z),(2y,z,x),(z,x,2y)] and A A^(T)=9I. If Tr(A) gt0 and xyz=(1)/(6) , then the vlaue of x^(3)+8y^(3)+z^(3) is equal to (where, Tr(A), I and A^(T) denote the trace of matrix A i.e. the sum of all the principal diagonal elements, the identity matrix of the same order of matrix A and the transpose of matrix A respectively)

A matrix which is not a square matrix is called a..........matrix.

Let A be a square matrix. Then which of the following is not a symmetric matrix -

Let A+2B=[{:(2,4,0),(6,-3,3),(-5,3,5):}] and 2A-B=[{:(6,-2,4),(6,1,5),(6,3,4):}] , then tr (A) - tr (B) is equal to (where , tr (A) =n trace of matrix x A i.e. . Sum of the principle diagonal elements of matrix A)

Let A be a 2 xx 2 matrix with non-zero entries and let A^2=I, where i is a 2 xx 2 identity matrix, Tr(A) i= sum of diagonal elements of A and |A| = determinant of matrix A. Statement 1:Tr(A)=0 Statement 2: |A| =1

Let R be a square matrix of order greater than 1 such that R is upper triangular matrix .Further suppose that none of the diagonal elements of the square matrix R vanishes. Then (A) R must be non singular (B) R^-1 does not exist (C) R^-1 is an upper triangular matrix (D) R^-1 is a lower triangular matrix

Let A be a square matrix of order 3 so that sum of elements of each row is 1 . Then the sum elements of matrix A^(2) is