Consider the linear system x6y4z5 2x10y9z4 x6y5z3 Solve the

Consider the linear system {x-6y-4z=-5 2x-10y-9z=-4 -x+6y+5z=3 Solve the linear system by row-reducing the corresponding augmented matrix Find the values of h for which the following set of vectors is linearly independent: {[1 0 0].[h 1 h][1 h 1]}.

Solution

solution -:

Your matrix

Find the pivot in the 1st column in the 1st row

Multiply the 1st row by 2

Subtract the 1st row from the 2nd row and restore it

Multiply the 1st row by -1

Subtract the 1st row from the 3rd row and restore it

Make the pivot in the 2nd column by dividing the 2nd row by 2

Multiply the 2nd row by -6

Subtract the 2nd row from the 1st row and restore it

Find the pivot in the 3rd column in the 3rd row

Multiply the 3rd row by -7

Subtract the 3rd row from the 1st row and restore it

Multiply the 3rd row by -1/2

Subtract the 3rd row from the 2nd row and restore it

Solution set:

x1 = -1

x2 = 2

x3 = -2

b) we will set up like that ( 1 h) ( h, 1)

we got 1-h^2 =0

h= plus / minus 1

	X1	X2	X3	b
1	1	-6	-4	-5
2	2	-10	-9	-4
3	-1	6	5	3