jonnyenglish
New member
- Joined
- Mar 13, 2019
- Messages
- 4
Hi,
I’m struggling to solve this equation by inverse matrix methods:
3v + 4u = 6
2u – v = -8
The booklet says the answer is: U = -1.8, V = 4.4 but I get V = -2.36, U = 3.27
I get the same answer as the booklet when solving by elimination, so it seems like I’m making a mistake when using the matrix method.
This is what I’ve done:
[MATH] \begin{bmatrix} 3 & 4\\ 2 & -1 \end{bmatrix}*\begin{bmatrix} v\\ u \end{bmatrix}=\begin{bmatrix} 6\\ -8 \end{bmatrix} [/MATH]
[MATH]\left | A \right | = (3*2) - (4*2) = -11[/MATH]
[MATH]Adj(A) = \begin{bmatrix} -1 & -4\\ -2 & 3 \end{bmatrix}[/MATH]
[MATH]\begin{bmatrix} V\\ U \end{bmatrix} = \frac{1}{-11} \begin{bmatrix} -1 & -4\\ -2 & 3 \end{bmatrix} * \begin{bmatrix} 6\\ -8 \end{bmatrix}[/MATH]
[MATH]= \frac{1}{-11} * \begin{bmatrix} 26\\ -36 \end{bmatrix}[/MATH]
[MATH]=\begin{bmatrix} -2.36\\ 3.27 \end{bmatrix}[/MATH]
Any help would be appreciated
I’m struggling to solve this equation by inverse matrix methods:
3v + 4u = 6
2u – v = -8
The booklet says the answer is: U = -1.8, V = 4.4 but I get V = -2.36, U = 3.27
I get the same answer as the booklet when solving by elimination, so it seems like I’m making a mistake when using the matrix method.
This is what I’ve done:
[MATH] \begin{bmatrix} 3 & 4\\ 2 & -1 \end{bmatrix}*\begin{bmatrix} v\\ u \end{bmatrix}=\begin{bmatrix} 6\\ -8 \end{bmatrix} [/MATH]
[MATH]\left | A \right | = (3*2) - (4*2) = -11[/MATH]
[MATH]Adj(A) = \begin{bmatrix} -1 & -4\\ -2 & 3 \end{bmatrix}[/MATH]
[MATH]\begin{bmatrix} V\\ U \end{bmatrix} = \frac{1}{-11} \begin{bmatrix} -1 & -4\\ -2 & 3 \end{bmatrix} * \begin{bmatrix} 6\\ -8 \end{bmatrix}[/MATH]
[MATH]= \frac{1}{-11} * \begin{bmatrix} 26\\ -36 \end{bmatrix}[/MATH]
[MATH]=\begin{bmatrix} -2.36\\ 3.27 \end{bmatrix}[/MATH]
Any help would be appreciated
