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
[tex]\left[\begin{array}{cc}2&1\\6&5\\\end{array}\right][/tex] [tex]\left[\begin{array}{c}x\\y\\\end{array}\right][/tex] = [tex]\left[\begin{array}{c}3\\1\\\end{array}\right][/tex]
Let A=[tex]\left[\begin{array}{cc}2&1\\6&5\\\end{array}\right][/tex] X= [tex]\left[\begin{array}{c}x\\y\\\end{array}\right][/tex] and B= [tex]\left[\begin{array}{c}3\\1\\\end{array}\right][/tex]
Then
AX= B
X= A⁻¹ B
where A⁻¹ = [tex]\frac{Adj A}{mod of A}[/tex] where A mod ≠ 0
Adj A= [tex]\left[\begin{array}{cc} 5&-1\\-6&2\\\end{array}\right][/tex]
A mod = 10-6=4
A⁻¹ = 1/4 [tex]\left[\begin{array}{cc} 5&-1\\-6&2\\\end{array}\right][/tex]
X= A⁻¹ B= 1/4 [tex]\left[\begin{array}{cc} 5&-1\\-6&2\\\end{array}\right][/tex] [tex]\left[\begin{array}{c}3\\1\\\end{array}\right][/tex]
X= 1/4 [tex]\left[\begin{array}{c} 5x3+-1x1\\-6x3+2x1\\\end{array}\right][/tex]
X= 1/4 [tex]\left[\begin{array}{c} 15-1\\-18+2\\\end{array}\right][/tex]
X= 1/4 [tex]\left[\begin{array}{c} 14\\-16\\\end{array}\right][/tex]
From the above x= 14/4 and y= -16/4
Matrix inversion method can also be understood
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