1. ## 3x3 matrix inverse

The matrix B is given by B = $\displaystyle \begin{pmatrix} a & 1 & 3\\ 2 & 1 & -1\\ 0 & 1 & 2 \end{pmatrix}$

Given that B is non-singular, find the inverse matrix $\displaystyle {B}^{-1}$.

2. Originally Posted by BabyMilo
The matrix B is given by B = $\displaystyle \begin{pmatrix} a & 1 & 3\\ 2 & 1 & -1\\ 0 & 1 & 2 \end{pmatrix}$

Given that B is non-singular, find the inverse matrix $\displaystyle {B}^{-1}$.
Set $\displaystyle \begin{pmatrix} a & 1 & 3 & |1 & 0 & 0\\ 2 & 1 & -1 & |0 & 1 & 0\\ 0 & 1 & 2 & |0 & 0 & 1 \end{pmatrix}$

Now use row operations to get the left hand side in identity form.
Your solution will be the resulting right hand side.

3. Solution:

B$\displaystyle ^{-1} =\begin{pmatrix} \frac{3}{3a+2} & \frac{1}{3a+2} & \frac{-4}{3a+2}\\ \frac{-4}{3a+2} & \frac{2a}{3a+2} & \frac{a+6}{3a+2}\\ \frac{2}{3a+2} & \frac{-a}{3a+2} & \frac{a-2}{3a+2} \end{pmatrix}$

4. Originally Posted by Anonymous1
Solution:

B$\displaystyle ^{-1} =\begin{pmatrix} \frac{3}{3a+2} & \frac{1}{3a+2} & \frac{-4}{3a+2}\\ \frac{-4}{3a+2} & \frac{2a}{3a+2} & \frac{a+6}{3a+2}\\ \frac{2}{3a+2} & \frac{-a}{3a+2} & \frac{a-2}{3a+2} \end{pmatrix}$
but some how the answer for a=-1

5. What do you mean???.. u asked for the inverse and the inverse that is given is correct.
Originally Posted by BabyMilo
but some how the answer for a=-1

6. Originally Posted by Dreamer78692
What do you mean???.. u asked for the inverse and the inverse that is given is correct.
unfortunately the mark scheme did not include, this question for some reason.

but in the examiner comment, it says a=-1

and this would be support by iii) if you use a=-1.

thanks for the help.

7. Originally Posted by BabyMilo
unfortunately the mark scheme did not include, this question for some reason.

but in the examiner comment, it says a=-1

and this would be support by iii) if you use a=-1.

thanks for the help.
The inverse given in post #3 is correct. You are meant to use it to answer part (iii). When a = -1, B corresponds to the coefficient matrix of the given linear system ....