00:01
Hello everyone, in this problem we are given with the u matrix and a matrix.
00:04
We need to find whether u in the plane r3 is spanned by the columns of a or not.
00:11
So, if u can be written as the linear combination of the columns of a, then u in the plane r3 can be spanned by the column of a.
00:20
So, u can be written as a of 5 minus 3 2 and plus b of minus 3 7 and so on.
00:35
So, now substituting the value of u here, so it would be 14 to 12 to be equal to a of 5 minus 3 2 plus b of minus 3 7.
00:57
So, now multiplying this we have the values of 14 to be equal to 5 a minus 3 b.
01:06
Let us take this to be equation number 1 and from the second row we have 2 to be equal to minus 3 a plus 7 b.
01:13
Let us take this to be equation number 2 and from the third row we can have 12 to be equal to 2 a plus 2 b.
01:22
Let us take this to be equation number 3.
01:24
So, now solving the equations 1 and 2, so from 1 and 2 multiplying equation 1 with 3 and the equation 2 with 5, we have the values to be 15 a minus 9 b to be equal to 42 and minus 15 a plus 35 b to be equal to 10.
01:58
Now, adding up these two values these two terms get cancelled and here we have 26 b to be equal to 52.
02:06
So, from this we have the value of b to be equal to 52 divided by 26 on dividing we have the value of b to be 2...