Test: Introduction To Matrices

= x+10 = 3x+4
= x = 3

Since, there are 2 rows and 2 columns in the matrix, order of the matrix is 2*2.

⇒ y² - 4y = -3

⇒ y² - 4y + 3 = 0

⇒ y² -3y - y +3 = 0

⇒ y (y - 3) -1 (y-3) = 0

⇒(y - 1) (y - 3) = 0

⇒ y = 1,3

But there is not such option

We have another equation:

⇒ 5y = 6y² + 1

⇒ 6y² -5y +1 = 0

⇒ 6y² -3y - 2y + 1 = 0

⇒ 3y (2y - 1) - 1 (2y - 1) = 0

⇒ (3y - 1) (2y - 1) = 0

⇒ y = 1/2, 1/3

Hence value of y is 1/2, 1/3.

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

3^2x2= 3⁴= 81

A matrix having non-zero elements only in the diagonal running from the upper left to the lower right.

The given matrix is a diagonal matrix. 

There are 2 rows and 5 columns in the matrix.
Therefore, order of the matrix: 2 x 5.

Rows are represented by i
Columns are represented by j
^._.. a=(i+3)(j-1)
i=2 , j=1    (given)
a₂₁ = (2+3)(1-1)=0
so, a=0

a_ij = 1/2 |i-3j|
As a_ij = a₂₂ ie i = 2 and j = 2
By substituting the values in the equation, we get
a₂₂ = 1/2 |2-3(2)| = 1/2 |-4| = 2 

Correct Answer : b

Explanation :  In general a 2×3 matrix is given by

A = [(a₁₁, a₁₂ , a₁₃) (a₂₁, a₂₂, a₂₃)]

Now, a_ij = |2i−3j|

The possible values of i = 1, 2 and j = 1, 2, 3