If A=[a(i j)] is a scalar matrix of o...

If `A=[a_(i j)]` is a scalar matrix of order `nxxn` such that `a_(i i)=k` for all `i` , then trace of `A` is equal to `n k` (b) `n+k` (c) `n/k` (d) none of these

n+k

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

MATRICES
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos
MATRICES
OBJECTIVE RD SHARMA ENGLISH|Exercise Section I - Assertion Reason Type|12 Videos
LOGARITHMS
OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|21 Videos
MEAN VALUE THEOREMS
OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|28 Videos

Similar Questions

Explore conceptually related problems

If A=[a_(ij)] is a scalar matrix of order nxxn and k is a scalar, then abs(kA)=

If A=[a_(i j)] is a 2xx2 matrix such that a_(i j)=i+2j , write A .

If S=[S_(i j)] is a scalar matrix such that s_(i i)= k and A is a square matrix of the same order, then A S=S A=? A^k (b) k+A (c) k A (d) k S

If S=[S_(i j)] is a scalar matrix such that s_(i i)=ka n dA is a square matrix of the same order, then A S=S A=? A^k (b) k+A (c) k A (d) k S

If A=[a_(i j)] is a square matrix of even order such that a_(i j)=i^2-j^2 , then (a) A is a skew-symmetric matrix and |A|=0 (b) A is symmetric matrix and |A| is a square (c) A is symmetric matrix and |A|=0 (d) none of these

If A is a square matrix of order n xx n and k is a scalar, then adj (kA) is equal to (1) k adj A (2) k^n adj A (3) k^(n-1) adj A (4) k^(n+1) adj A

Let A=[a_(ij)] be a square matrix of order n such that {:a_(ij)={(0," if i ne j),(i,if i=j):} Statement -2 : The inverse of A is the matrix B=[b_(ij)] such that {:b_(ij)={(0," if i ne j),(1/i,if i=j):} Statement -2 : The inverse of a diagonal matrix is a scalar matrix.

If A is a square matrix of order nxxn and lamda is a scalar then |lamdaA| is (A) lamda|A| (B) lamda^n|A| (C) |lamda||A| (D) none of these

A =([a_(i j)])_(mxxn) is a square matrix, if (a) m n (c) m =n (d) None of these

OBJECTIVE RD SHARMA ENGLISH-MATRICES-Exercise

If A=[a(ij)] is a scalar matrix, then trace of A is
Text Solution
|
If A=[a(i j)] is a scalar matrix of order nxxn such that a(i i)=k f...
Text Solution
|
If A=[a(i j)] is a scalar matrix of order nxxn such that a(i i)=k f...
Text Solution
|
If A=[a(ij)] is a scalar matrix of order nxxn and k is a scalar, then ...
Text Solution
|
If f(alpha)=[[cosalpha,-sinalpha,0],[sinalpha,cosalpha,0],[ 0, 0, 1]],...
Text Solution
|
If F(x)=[("cos"x,-sin x,0),(sin x,cos x,0),(0,0,1)] and G(y)=[(cos y,0...
Text Solution
|
Find the matrix A satisfying the matrix equation [{:(2,1),(3,2):}]A[...
Text Solution
|
If [(1,-tantheta),(tantheta,1)][(1,tantheta),(-tantheta,1)]^(-1)=[(a,-...
Text Solution
|
If A and B are two matrices such that A+B and AB are both defind, then
Text Solution
|
If a matrix A is such that 3\ A^3+2\ A^2+5\ A+I=0 , then A^(-1) is equ...
Text Solution
|
Let A and B be matrices of order 3 xx 3. If AB = 0, then which of the ...
Text Solution
|
If A is an invertible matrix, then which of the following is correct
Text Solution
|
Which of the following is/are incorrect? (i) adjoint of a symmetri...
Text Solution
|
If [[alpha, beta], [gamma, -alpha]] is to be square root of two-rowed ...
Text Solution
|
If for matrix A,A^(2)+l=0, where l is the identity matrix, then A equa...
Text Solution
|
If A=[a(ij)](mxxn) is a matrix of rank r then (A) r=min{m,n} (B) rlemi...
Text Solution
|
If In is the identity matrix of order n, then rank of In is
Text Solution
|
A=[a(ij)](mxxn) is a square matrix, if
Text Solution
|
The rank of a null matrix is
Text Solution
|
If A is a matrix such that there exists a square submatrix of order r ...
Text Solution
|