Question

Solve by using matrix inversion method 2x+y^3,6x+5y=1

Answer 1

Matrix inversion method can be used when the matrix A is square and non singular.

Square matrix is one which has equal number of rows and columns.

Non singular matrix is one whose determinant value is not equal to zero.

x= 14/4 and y= -16/4

2x+y=3 ---------eq. A

6x+5y=1--------eq.B

The above equations can be written in the form of matrices as follows

$\left[\begin{array}{cc}2&1\\6&5\\\end{array}\right]$  $\left[\begin{array}{c}x\\y\\\end{array}\right]$ = $\left[\begin{array}{c}3\\1\\\end{array}\right]$

Let  A=$\left[\begin{array}{cc}2&1\\6&5\\\end{array}\right]$     X=  $\left[\begin{array}{c}x\\y\\\end{array}\right]$  and B= $\left[\begin{array}{c}3\\1\\\end{array}\right]$

Then

AX= B

X= A⁻¹ B

where A⁻¹ = $\frac{Adj A}{mod of A}$  where A mod ≠ 0

Adj A= $\left[\begin{array}{cc} 5&-1\\-6&2\\\end{array}\right]$

A mod = 10-6=4

A⁻¹ = 1/4  $\left[\begin{array}{cc} 5&-1\\-6&2\\\end{array}\right]$

X= A⁻¹ B= 1/4  $\left[\begin{array}{cc} 5&-1\\-6&2\\\end{array}\right]$ $\left[\begin{array}{c}3\\1\\\end{array}\right]$

X= 1/4  $\left[\begin{array}{c} 5x3+-1x1\\-6x3+2x1\\\end{array}\right]$

X= 1/4  $\left[\begin{array}{c} 15-1\\-18+2\\\end{array}\right]$

X= 1/4  $\left[\begin{array}{c} 14\\-16\\\end{array}\right]$

From the above x= 14/4 and y= -16/4

Matrix inversion method can also be understood

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