Solve for x1 and x2

frctl

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Picture1.png

I require help with this system the way it is presented
Where does the x1 and x2 go or with which coefficient?
 

Romsek

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You've never seen matrices before?
 

frctl

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Yes I am learning them right now.
 

Romsek

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well just apply matrix subtraction and multiplication as you usually would.
First subtract \(\displaystyle \begin{pmatrix}3\\4\end{pmatrix}\) from both sides then the first equation is

\(\displaystyle 1 \cdot x_1 + 2 \cdot x_2 = 6\)

I leave you to figure out the second equation
 

frctl

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1 · x1 + 2 · x2 = 6
1 · x1 + 1 · x2 = 5

This is not the answer
 

pka

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View attachment 17443

I require help with this system the way it is presented
Where does the x1 and x2 go or with which coefficient?
View attachment 17443

I require help with this system the way it is presented
Where does the x1 and x2 go or with which coefficient?
\(\left[ {\begin{array}{*{20}{c}} 1&2 \\ 1&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} x \\
y \end{array}} \right] + \left[ {\begin{array}{*{20}{c}} 3 \\ 4 \end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
9 \\ 9 \end{array}} \right]\) Subtract from both sides.
\(\left[ {\begin{array}{*{20}{c}} 1&2 \\ 1&1 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} x \\
y \end{array}} \right] = \left[ {\begin{array}{*{20}{c}}
6 \\ 5 \end{array}} \right]\) Find the inverse.
\(\left[ {\begin{array}{*{20}{c}} x \\ y \end{array}} \right]=\left[ {\begin{array}{*{20}{c}} 1&2 \\ 1&1 \end{array}} \right]^{-1} \left[ {\begin{array}{*{20}{c}} 6 \\ 5 \end{array}} \right]\)
 

frctl

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I found the inverse is

-1 2
1 -1

How does this help me solve for x1 and x2
 

frctl

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Ah wait if I multiply them out I obtain

x1 = 4
x2 = 1
 

Subhotosh Khan

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frctl

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How do I check my answer in this case
 

pka

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How do I check my answer in this case
Go on, frctl, don't be obtuse. Substitute the values into the equation in the OP. See if they work.
 

frctl

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Yes I obtain
6
5

Thank you
 

frctl

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the matrix
x1 and x2
 

Otis

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the matrix
x1 and x2
That's not correct, frctl. You already posted your solution: x1=4 and x2=1 (post #8).

The second equation in post #6 shows the matrix containing elements 6 and 5.

We need to be more careful with language.

😎
 
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