00:01
Hello students in this question we have to find whether the vectors a b c d are linearly independent or not so we write it in the form a a plus b b plus c c plus d is equal to 0 to find a b b we write the vectors in the form of a matrix that is minus 2 4 minus 1 6 0 1 1 1 1, 4, 2, minus 5, 3, 3, 4, minus 6, 1, 19.
00:45
Multiply by a, b, c, d is equal to 0 vector.
00:57
We apply some row transforms to this matrix.
01:02
Apply r4 minus 3 r1 on r3 we apply r3 minus 1 by 2 r1 on r2 we apply r3 minus 1 by 2 r1 on r2 we apply r2 my plus 2 r1 so this matrix will become minus 2 0 0 0 1 0 1 4, 2 minus 1, 2 minus 3, 4, 2 minus 1, 7.
02:03
Multiply by a, b, c, d is equal to 0 vector.
02:12
We apply some more row transforms on r4, r4 minus 4r2, r3, r3 minus r2, r2, the matrix will become minus 2 -0 -0 -0 -1 -0 -0 -0 -0 -0 -0 -0 -1 -2 -1 -3 -1 4 -2 -2 -2 -m minus 3 -1 a, b, c, d is equal to 0 -0 -0 -0 -0.
03:06
We apply some more row transforms to this, that is on r4 we apply r4 minus 1 by 3 r3.
03:25
The matrix will become minus 2 0000 0100, 2 minus 1 ,0, 2 minus 1, 3 0 ,000, 2 minus 1, 3 0, 0, 2 ,000, 3 0, 2 ,000, 3, 0, 2, minus 3 0 a b c d 0 vector we multiply first row by 2 divide first row by 2 and the third row by 3 so we have minus 1 0 0 0 0 0 0 1 0 0 0 0 0 1 minus 1 1 0 0 0 0 0 0 0 0 1 minus 1 1 0 0 0 0 0 0 2 2 2 2 2 2 2 minus 1 0.
04:34
From here we get three equations...