Question

What is the solution of the matrix equation?

Answer 1

By solving a system of equations, we will see that matrix X is:

$X = \left[\begin{array}{ccc}-5&9\\26&-60\end{array}\right]$

How to find matrix X?

X will be a matrix, let's define:

$X = \left[\begin{array}{ccc}x_{11}&x_{12}\\x_{21}&x_{22}\end{array}\right]$

Replacing that in the given equation we will get a system of equations:

9*x₁₁ + 4*x₂₁ = -9

2*x₁₁ + 1*x₂₁ = -1

9*x₂₁ + 4*x₂₂ = -6

2*x₂₁ + 1*x₂₂ = -8

We just need to solve that system of equations.

Using the second one we can write:

2*x₁₁ + 1*x₂₁ = -1

x₂₁ = -1 - 2x₁₁

Now we can replace that in the first equation:

9*x₁₁ + 4*x₂₁ = -9

9*x₁₁ + 4*(-1 - 2x₁₁ ) = -9

9*x₁₁ - 8*x₁₁ - 4 = -9

x₁₁ = -9 + 4 = -5

Then:

x₂₁ = -1 - 2x₁₁  = -1 - 2*(-5) = -1 + 10 = 9

So we just found the first two values of the matrix, now let's find the other two.

Using the other two eqations:

9*x₂₁ + 4*x₂₂ = -6

2*x₂₁ + 1*x₂₂ = -8

We rewrite the second as:

x₂₂ = -8 - 2x₂₁

And replace that in the other one:

9*x₂₁ + 4*(-8 - 2x₂₁) = -6

x₂₁ - 32 = -6

x₂₁ = -6 + 32 = 26

Then:

x₂₂ = -8 - 2x₂₁ = -8 - 2*26 = -60

Then our matrix is:

$X = \left[\begin{array}{ccc}-5&9\\26&-60\end{array}\right]$

Learn more about systems of equations:

brainly.com/question/13729904

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