00:01
So, we have to determine the basis of subspace of r cube consisting over all the vectors of the form a, 2b, a plus the rise of d.
00:16
So, what will be the dimension of this subspace? that is also we have been asked.
00:22
So, first of all, let us assume a is a matrix of the form having the elements, let's suppose 1, 0, 1, 0, 0, 2, 0 and here it will be 3, 0.
00:39
Now applying the row operation that is r3 with tends to the r3 minus of r1.
00:47
So, this will be goes to.
00:49
So, what we are doing r3 minus r1.
00:51
So, 1 minus 1, 0, 3 minus 0, 3, 0 minus 0, 0.
00:57
Got it? so, here we will get 1, 0, 0, 0, 1, 0 all the terms will be same, but only this term is going to be 0, 2, 0 and here it will be 0, 3, 0.
01:14
Now we use the second operation r3 with tends to r3 divided by 3 and r2 tends to r2 divided by 2.
01:24
That is 0 operation.
01:25
So, this can be equals to the 1, 0, 0, 0, 1, 0, 0, 1, 0.
01:34
Because we are dividing it second and third by 2 and 3...