The system of linear equations 2xy 12 12x 6y 3 have a uni

The system of linear equations 2x-y = 1/2 12x - 6y = 3 have a unique solution. If A is 2 x 3 and B is 3 x 4 matrix, then (AB)T is the matrix of the size 4x2. is lower triangular but not upper triangular. The determinant of the matrix The absolute values of minors and cofactors of the elements of a square matrix are identical.

Solution

a) 2x -y =1/2

12x -6y = 3

Divide equation by2:

2x - y = 1/2

Both equations are same ;

So, there are inifinite solutions

FALSE

b) A ---2 x3 ; B --- 3x4 ; AB ---2 x 4

(AB)^T ----> 4 x 2

TRUE

c) [ -1 2 , 0 1]

Determinant = -1*1 +2*0 = -1

The detrminat is non -zero , so it is invertible matrix

d) It is a diagonal matrix with zero elements below and above the diagonal

FALSE

e)[ 1 0 1 , 2 1 4 , 3 0 3 ]

Detreminant = 1(3 -0 ) - 0( ) +1(0 -3)

= 3 -3 =0

FALSE