State whether the following statements are true or false 6 a

State whether the following statements are true or false: [6]
(a) Every system of linear equation is consistent.
(a)
(b) The addition of two matrices is not possible only when there order differs.
(b)
(c) The transpose of a lower triangular matrix is again lower triangular matrix.
(c)
(d) If A =

3 0
0 1

and B =

2 0
0 4
, then AB =

6 0
0 4

(d)
(e) The determinant of every non-singular matrix is zero.
(e)
(f) The absolute values of minors and cofactors of the elements of a square matrix are
not identical.
(f)

Solution

a) False .As if no.of equations outcomes the no. Of constraints & no equation is linear combination of other equations ,it will be inconsistent.

B)true. Two matrix can be add or subtract if both matrix are of same order.

C)false. The transpose of lower triangular matrix is upper triangular matrix & vice versa.

D)true

If A=. 3 0 B=2 0 AB=6 0

0 -1 0 4 0 -4

E)False. The determinant of singular matrix is always zero.

F)false