Introduction to Matrices and its Operations (May 3) - JEE MCQ

The number of rows (m) and the number of columns (n) in the given matrix A= 

is 2. Therefore, the order of the matrix is 2×2(m×n).

The number of elements for a matrix with the order m×n is equal to mn, where m is the number of rows and n is the number of columns in the matrix.

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

The number of possible entries of 2 × 2 matrix is 4 Every entry has two choice, 0 or 1.

Thus, the total no. of choices is,

2 × 2 × 2 × 2 = 2⁴

= 16

As the given two matrices are 3x3 and 3x1 respectively
hence, the product will be a 3x1 matrix
so, {(1*0+ 2*2+ 0*x) (2*0+ 0*2+ 1*x) (1*0+ 0*2+ 2*x)}
= {4, x, 2x} as a 3x1 matrix

If A, B are, respectively m × n, k × l matrices, then both AB and BA are defined if and only if n = k and l = m. In particular, if both A and B are square matrices of the same order, then both AB and BA are defined.

A = [2, 3, 4]  
Therefore AXB = {(2*1) + (3*(-1)) + (4*2)}
AXB = {2 + (-3) + 8}
AXB = 7