Question

In: Math

Solve the linear system of equations Ax = b, and give the rank of the matrix...

Solve the linear system of equations Ax = b, and give the rank of the matrix A, where A =

1 1 1 -1
0 1 0 2
1 0 1 1

b =

1
2
3

Solutions

Expert Solution

augmented matrix is

1 1 1 -1 1
0 1 0 2 2
1 0 1 1 3

convert into Reduced Row Eschelon Form...

Add (-1 * row1) to row3

1 1 1 -1 1
0 1 0 2 2
0 -1 0 2 2


Add (1 * row2) to row3

1 1 1 -1 1
0 1 0 2 2
0 0 0 4 4


Divide row3 by 4

1 1 1 -1 1
0 1 0 2 2
0 0 0 1 1


Add (-2 * row3) to row2

1 1 1 -1 1
0 1 0 0 0
0 0 0 1 1


Add (1 * row3) to row1

1 1 1 0 2
0 1 0 0 0
0 0 0 1 1


Add (-1 * row2) to row1

1 0 1 0 2
0 1 0 0 0
0 0 0 1 1

reduced system is

there are 3 pivot entry at first second and fourth column

hence rank is 3

.

....................free

general solution is


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