math111_logo Augmented Matrix


Exercise Find the augmented matrices.

2x1 - 3x2 - x3 = 3
x1 + x2 + 2x3 = -1
x1 + 2x2 + 3x3 + 4x4 = 5
x1 + 2x2 = 3
4x1 + 5x2 = 6
7x1 + 8x2 = 9
x1 + 3x2 + 2x3 + x5 = 0
- x1 - x2 - x3 + x4 = 1
4x2 + 2x3 + 4x4 + 3x5 = 3
x1 + 3x2 + 2x3 - 2x4 = 0

Answer

Exercise Recover systems of linear equations from the augmented matrices.

[ 1 3 5 ]
2 4 6
[ 2 5 ]
[ 1 1 ]
2 2
3 3
4 4
[ a 1 1 ]
1 a 1
1 1 a
[ 1 0 0 0 4 ]
0 1 0 0 5
0 0 1 0 6
0 0 0 1 7
[ 0 0 0 0 0 ]
0 2 0 -3 4
1 -1 5 0 8

Answer

Exercise The identity matrix I is the square matrix with 1 on the diagonal and 0 off diagonal. For example, the 3 by 3 identity matrix is

I3 = [ 1 0 0 ]
0 1 0
0 0 1

Show that the system of equations corresponding to the augmented matrix [In b] is x = b.