Question

PLZZ HELPPP

Which matrix equation can be used to solve the system?
x+y=21
5x+4y=20

Answer 1

`X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\`

Explanation:

Given the simultaneous equation

x+y=21

5x+4y=20

To write in matrix form, it must be in the form AX= b

X = A⁻¹b

A⁻¹ is the inverse of matrix A

A is a 2by2 matrix

X is the variables

b is a column matrix

The expression will therefore be written as;

`A=\left[\begin{array}{ccc}1&1\\5&4\\\end{array}\right] \\\\|A| = 1(4)- 5(1)\\|A| = 4-5\\|A| = -1\\A^(-1) = -\left[\begin{array}{ccc}4&-1\\-5&1\\\end{array}\right] \\\\A^(-1) = \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \\`

Hence the required product matrix that represent X is;

`X= \left[\begin{array}{ccc}-4&1\\5&-1\\\end{array}\right] \left[\begin{array}{ccc}21\\20\\\end{array}\right] \\`