Invertible Matrices

Determine the inverse of these matrices if one exists


1.

A=(3648)A−1=?\displaystyle A = \left(\begin{matrix} 3 & 6 \\ 4 & 8 \end{matrix}\right) \\[3mm] A^{-1} = ?

Solution:

Find the determinant

=(3)(8)−(4)(6)=24−24=0\displaystyle \\[3mm] = (3)(8) - (4)(6) \\[2mm] = 24 - 24 \\[2mm] = 0

If the determinant is zero the matrix cannot be invertible. One reason follows from a method to invert a matrix one multiplies by 1/determinant. A 1/0 is undefined


Answer:

Matrix is not invertible. Ie has no inverse.





Question Content