Matrices - Online Test

Answer : Option C
Explaination / Solution:

If A and B are symmetric matrices of the same order, then AB + BA is always a symmetric matrix.

Answer : Option C
Explaination / Solution:

23x3=29=512.

The number of elements in a 3 X 3 matrix is the product 3 X 3=9.

Each element can either be a 0 or a 1.

Given this, the total possible matrices that can be selected is 29=512

Answer : Option B
Explaination / Solution:

It is an identity matrix with the order 2*2, I2=[1001]

Answer : Option B
Explaination / Solution:

Here, matrix P is of order 2 × 3 and matrix Q is of order 3 × 2 , then , the product PQ is defined only when : no. of columns in P = no. of rows in Q. And the order of resulting matrix is given by : rows in P x columns in Q.

Answer : Option A
Explaination / Solution:

The number of elements in a 2 x 2 matrix is the product 2 x 2 =4

Each element can either be a 0,1 or 2.

Given this, the total possible matrices that can be selected is 34

32x2= 34= 81

Answer : Option A
Explaination / Solution:

A square matrix A for whichAn= 0, where n is a positive integer, is called a Nilpotent matrix.

The determinant and trace of the matrix is always Zero for a Nilpotent Matrix.

For the given matrix "A", determinant (A)=0 and trace(A)=0.

Answer : Option B
Explaination / Solution:

In a diagonal matrix all elements except diagonal elements are zero.i.e. aij= 0 , iffi ≠ j.

Answer : Option C
Explaination / Solution:

If two rows or column of a matrix are identical then determinant of such a matrix is zero.

Answer : Option A
Explaination / Solution:

[xyz]1 x 3 ⎡⎣⎢ahghbfgfc⎤⎦⎥3x3⎡⎣⎢xyz⎤⎦⎥3x1= [A]1 x 1${\left[A\right]}_{1x1}$ . ( where ; matrix A denotes the product of three given matrices.)

Answer : Option B
Explaination / Solution:

Only a null matrix can be symmetric as well as skew symmetric.

In Symmetric Matrix AT =A,

    Skew Symmetric Matrix AT = -A,

    Given that the matrix is satisfying both the properties therefore Equating the RHS we get A= -A i.e 2A=0 .

   Therefore A=0,which is a null matrix.