00:01
In this problem, it is said that c is an m by n matrix and k is a scalar, so that k times c is equal to 0.
00:07
Now, we need to determine which of the given statements are correct.
00:11
Now, the first statement is that either k is 0 or c is 0, and the second statement is that k is not 0 and c is not the 0 matrix.
00:19
So, first of all, let us consider c.
00:21
It is an m by n matrix.
00:25
So let us consider the elements to be like this, a11, a1, a1, 2.
00:30
And we go up to a1n because it's an m by n matrix, so there will be n columns, and we'll continue like this until we have am1, am2, and we go up to amn.
00:44
So this is c.
00:45
And if we consider kc, then we multiply k with this.
00:50
And how do we multiply a scalar with a matrix? we just multiply each element of the matrix by k.
01:00
Now, if this is the zero matrix, then that will mean that each of these elements is zero.
01:07
So if each of the elements are zero, if we consider just this first one, if k -a -1 -1 is zero, then using the zero product property, that means that k is zero or a -1 -1 is zero.
01:19
So we can see that statement a -1 is correct because k might be zero...