Test: Introduction To Matrices

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 these are not real numbers.

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.

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