00:01
In a part of the question, we are given a matrix a.
00:07
And the order of matrix is given us 4 cross 5.
00:12
Also we are given rank of matrix a is equals to 3.
00:18
And we have to find dimension of column space a.
00:22
So as we know, rank of a must be equal to dimension of column space.
00:34
Of a.
00:35
So from here we have dimension of column space of a is equals to 3 as the rank of matrix a is 3.
00:46
So this is the final answer for a part of the question.
00:50
Now moving towards the b part of this question here we are given matrix a.
00:58
The order of this matrix is 5 cross 6.
01:02
Here dimension of null space of of a is given as 2 and we have to find dimension of row space of 2.
01:14
So as we know dimension of row space sorry row space of a is equals to number of columns minus dimension of null space of a.
01:35
This is equals to number of columns are 6 minus dimension of null space of a.
01:42
Of a is 2.
01:43
6 minus 2 is 4 so from here we can say dimension of row space of a is equals to 4 and this is the final answer for b part of the question...