3 Solve the systems of equations using the GaussJordan metho

3. Solve the systems of equations using the Gauss-Jordan method: (a) r 4y 22 39, (b) r 4y 22 9, 22 13. -2a 4y 2 11, (c) 5y 42 31 z 2a: 32 4. Let U be the set of all vectors u in R4 such that 2u1 3u3 2u4 0 (i.e. U is the solution space of given system) (a) Find the dimension of U. (b) Find a basis of U. (c) Write U using this basis.

Solution

(a)

Your matrix

Find the pivot in the 1st column and swap the 2nd and the 1st rows

Multiply the 1st row by -2

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

Multiply the 1st row by 3

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

Make the pivot in the 2nd column by dividing the 2nd row by 5

Multiply the 2nd row by 4

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

Multiply the 2nd row by -5

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

The system is inconsistent

?	X1	X2	X3	b
1	-2	-3	1	2
2	1	4	2	9
3	3	7	1	6