Question

Help:

The matrix equation represents a system of equations.

A matrix with 2 rows and 2 columns, where row 1 is 2 and 5 and row 2 is 1 and 3, is multiplied by matrix with 2 rows and 1 column, where row 1 is x and row 2 is y, equals a matrix with 2 rows and 1 column, where row 1 is 7 and row 2 is 5.

Solve for x and y using matrices. Show or explain all necessary steps.

Answer 1

(x,y)=(-4,3)

Explanation:

[2 5][x] = [7]

[1 3][y] [5]

[2 5 | 7] <-- Write the augmented matrix

[1 3 | 5]

[1 5/2 | 7/2] <-- (1/2)R1

[1 3 | 5 ]

[1 5/2 | 7/2] <-- R2-R1

[0 1/2 | 3/2]

[1 5/2 | 7/2] <-- 2R2

[0 1 | 3 ]

[1 0 | -4 ] <-- R1-(5/2)R2

[0 1 | 3 ]

RREF is achieved using Gaussian-Jordan Elimination. Therefore, the solution is (-4,3).