MATRICES

Question 1

Row matrix

Answer 1

The no. of rows in a matrix is 1

Question 2

Column matrix

Answer 2

The no. of columns in a matrix is 1.

Question 3

Null matrix

Answer 3

All the elements in a matrix should be zero.

Question 4

Square matrix

Answer 4

The no. of rows should be equal to the no. of columns.

Question 5

Upper matrix

Lower matrix

Answer 5

The elements of the lower triangle part of the matrix should be zero.

The elements of the upper triangle part of the matrix should be zero.

Question 6

Diagonal matrix

Answer 6

All elements except the diagonal should be zero. If (d1,d2,d3 are equal, then it is a scalar matrix.)

Question 7

Unit matrix

Answer 7

If all the diagonals of the matrix are equal to one.

Question 8

Singular matrix

Answer 8

The determinant of the matrix is equal to 0.

Question 9

Trace of a matrix

Answer 9

The sum of all the principal diagonal elements of the matrix.

Question 10

Properties of the Trace of a Matrix

Answer 10

1. Tr(A+B)= Tr(A)+Tr(B)
2. Tr(KA)=k.Tr(A)
3. Tr(AB)=Tr(A).Tr(B)

Question 11

If A is a square matrix, then :

Answer 11

A^n.A^m=A^n+m

Question 12

Properties of Determinant of a Matrix

Answer 12

1. |KA|=K^n|A|
2. |A^2|=|A|^2
3. |AB|=|A||B|

Question 13

Characteristics Equation

Answer 13

|A-ΛI|=0

Question 14

STANDARD MATRIX

Answer 14

1. IDEMPOTENET MATRIX: a square matrix that, when multiplied by itself, results in the original matrix
2. ENVOLUTARY MATRIX: a matrix on squaring becomes identity matrix.
   3.NILPOTENT MATRIX: if some value of K gives the value as 0, the degree should be greater than 1. A^k=0 then k>1.

Question 15

Periodic matrix

Answer 15

if A^2, then the period is 1, IF A^3 then period is 2.