Home
Class 12
MATHS
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

A

`k^(n)`

B

`n/k`

C

nk

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    DISHA PUBLICATION|Exercise Exercise 1: Concept Builder (Topic 2)|23 Videos
  • MATRICES

    DISHA PUBLICATION|Exercise Exercise 1: Concept Builder (Topic 3)|23 Videos
  • MATRICES

    DISHA PUBLICATION|Exercise Exercise 2: Concept Applicator|30 Videos
  • MATHEMATICAL REASONING

    DISHA PUBLICATION|Exercise Exercise-2 : Concept Applicator|30 Videos
  • PRINCIPLE OF MATHEMATICAL INDUCTION

    DISHA PUBLICATION|Exercise Exercise-2 Concept Applicator|20 Videos

Similar Questions

Explore conceptually related problems

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

If A=[a_(ij)]_(3xx3) is a scalar matrix such that a_(ij)=5" for all "i=j," then: "|A|=

If k is a scalar and I is unit matrix of order 3, then adj(kI)=

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.

Let A_(r) denote a scalar matrix of order n xx n with each diagonal element as r.Then,the trace of the matrix (A_(1)A_(2)A_(3)...A_(n)), is

Lt_(nrarroo) {(n!)/(kn)^n}^(1/n), k!=0 , is equal to (A) k/e (B) e/k (C) 1/(ke) (D) none of these

A square matrix [A_(ij)] such that a_(ij)=0 for I ne j and a_(ij)=k where k is a constant for i=j is called.

A square matrix [a_(ij)] such that a_(ij)=0 for i ne j and a_(ij) = k where k is a constant for i = j is called :