Home
Class 12
MATHS
Let M be a column vector (not null vecto...

Let M be a column vector (not null vector) and `A=(MM^T)/(M^TM)` the matrix A is : (where `M^T` is transpose matrix of M)

A

idempotant

B

nilpotent

C

involutary

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • MATRICES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-2 : One or More than One Answer is/are Correct|5 Videos
  • MATRICES

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-3 : Matching Type Problems|4 Videos
  • LOGARITHMS

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|19 Videos
  • PARABOLA

    VIKAS GUPTA (BLACK BOOK) ENGLISH|Exercise Exercise-5 : Subjective Type Problems|3 Videos

Similar Questions

Explore conceptually related problems

If the order of matrix A is m xx n, then the order of the transpose of matrix A is :

Let A and B be two matrices such that the order of A is 5xx7 . If A^(T)B and BA^(T) are both defined, then (where A^(T) is the transpose of matrix A)

Let M be a 2xx2 symmetric matrix with integer entries. Then M is invertible if The first column of M is the transpose of the second row of M The second row of M is the transpose of the first column of M M is a diagonal matrix with non-zero entries in the main diagonal The product of entries in the main diagonal of M is not the square of an integer

Define a symmetric matrix. Prove that for A=[2 4 5 6] , A+A^T is a symmetric matrix where A^T is the transpose of Adot

If A=[[4,1],[5,8]] , show that A+A^T is symmetric matrix, where A^T denotes the transpose of matrix A

If A=[[2,4],[5,6]] , show that (A-A^T) is a skew symmetric matrix, where A^T is the transpose of matrix A.

Let A be a square matrix. Then prove that (i) A + A^T is a symmetric matrix, (ii) A -A^T is a skew-symmetric matrix and (iii) AA^T and A^TA are symmetric matrices.

Let A be a square matrix. Then prove that (i) A + A^T is a symmetric matrix, (ii) A -A^T is a skew-symmetric matrix and (iii) AA^T and A^TA are symmetric matrices.

Let a be square matrix. Then prove that A A^(T) and A^(T) A are symmetric matrices.

Let M be a 2xx2 symmetric matrix with integer entries. Then M is invertible if a. The first column of M is the transpose of the second row of M b. The second row of M is the transpose of the first column of M c. M is a diagonal matrix with non-zero entries in the main diagonal d. The product of entries in the main diagonal of M is not the square of an integer