# Thread: Matrix questions

1. ## Matrix questions

How can I calculate the X and AX?

Thank you so much, your help!!

2. ## Re: Matrix questions

Matrix multiplication:

$\displaystyle \left[\begin{matrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9\end{matrix}\right]\left[\begin{matrix} 1 & 2 & 3\\ 4 & 5 & 6\\ 7 & 8 & 9\end{matrix}\right]$

$\displaystyle =\left[\begin{matrix} (1 * 1) + (2 * 4) + (3 * 7) & (1 * 2) + (2 * 5) + (3 * 8) & (1 * 3) + (2 * 6) + (3 * 9)\\ (4 * 1) + (5 *4) + (6 * 7) & (4 * 2) + (5 * 5) + (6 * 8) & (4 * 3) + (5 * 6) + (6 * 9)\\ (7 * 1) + (8 * 4) + (9 * 7) & (7 * 2) + (8 * 5) + (9 * 8) & (7 * 3) + (8 * 6) + (9 * 9)\end{matrix}\right]$

$\displaystyle =\left[\begin{matrix}30 & 36 & 42\\ 66 & 81 & 96\\ 102 & 126 & 150\end{matrix}\right]$

For more information you can take a look at step by step multiplication at Matrix Multiplication Calculator

And solving linear equations using Gauss Jordan elimination method you can look at Gauss-Jordan Elimination Calculator

3. ## Re: Matrix questions

You can multiply $\displaystyle \begin{bmatrix}1 & 2 & -1 \\ 4 & -4 & 3 \\ -2 & 0 & 1 \end{bmatrix}\begin{bmatrix}1 & 1 & 3 \\ 4 & 2 & 3 \\ 1 & 1 & 1 \end{bmatrix}=$$\displaystyle \begin{bmatrix}1(1)+ 2(4)- 1(1) & 1(1)+ 2(2)- 1(1) & 1(3)+ 2(3)- 1(1) \\ 4(1)- 4(4)+ 3(1) & 4(1)- 4(2)+ 3(1) & 4(3)- 4(3)+ 3(1) \\ -2(1)+ 0(4)+ 1(1) & -2(1)+ 0(2)+ 1(1) & -2(3)+ 0(3)+ 1(1)\end{bmatrix}=$$\displaystyle \begin{bmatrix} 8 & 4 & 8 \\ 9 & -1 & 3 \\ -1 & -1 & -5 \end{bmatrix}$.

However, it is impossible to multiply that 3 by 3 matrix by the "1 by 4" matrix $\displaystyle \begin{bmatrix}x_1 \\ x_2 \\ x_3 \\ x_4 \end{bmatrix}$ so there is NO "X" and so NO "AX".