Mathematics: How can you solve equation with squares and cube

x=-7, y=2Step-by-step explanation:You are given the matrix equation Find the inverse matrix for the matrix 1. The determinant is2. 3. Inverse matrix isSo, the solution of the equation is...

How can you solve equation with squares and cube - id4735477, forschoolok123456789

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raedusty3200

07.01.2021

Mathematics

x=-7, y=2

Step-by-step explanation:

You are given the matrix equation

$\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right] \cdot \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}-18\\13\end{array}\right]$

Find the inverse matrix for the matrix

$\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right]$

1. The determinant is

$\left|\left[\begin{array}{cc}2&-2\\-1&3\end{array}\right]\right|=2\cdot 3-(-1)\cdot (-2)=6-2=4$

$a_{11}=2 \Rightarrow A_{11}=3\\ \\a_{12}=-2 \Rightarrow A_{12}=-(-1)=1\\ \\a_{21}=-1 \Rightarrow A_{21}=-(-2)=2\\ \\a_{22}=3 \Rightarrow A_{22}=2$

3. Inverse matrix is

$\dfrac{1}{4}\left[\begin{array}{cc}3&1\\2&2\end{array}\right]^T=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right]$

So, the solution of the equation is

$\left[\begin{array}{c}x\\y\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{cc}3&2\\1&2\end{array}\right]\cdot \left[\begin{array}{c}-18\\13\end{array}\right]=\\ \\=\dfrac{1}{4}\left[\begin{array}{cc}3\cdot(-18)+2\cdot 13\\1\cdot (-18)+2\cdot 13\end{array}\right]=\dfrac{1}{4}\left[\begin{array}{c}-28\\8\end{array}\right]=\left[\begin{array}{c}-7\\2\end{array}\right]$

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How can you solve equation with squares and cube

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