# SOLUTION: Can you help me solve the matrix equation. {{{matrix(1,3,(matrix(2,2,2,4,0,1))X, "=", (matrix(2,3,4,0,6,3,-1,5)))}}}

Algebra ->  Algebra  -> Matrices-and-determiminant -> SOLUTION: Can you help me solve the matrix equation. {{{matrix(1,3,(matrix(2,2,2,4,0,1))X, "=", (matrix(2,3,4,0,6,3,-1,5)))}}}      Log On

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 Algebra: Matrices, determinant, Cramer rule Solvers Lessons Answers archive Quiz In Depth

Question 176018This question is from textbook Algebra 2
: Can you help me solve the matrix equation.
This question is from textbook Algebra 2

Found 3 solutions by Mathtut, jim_thompson5910, Edwin McCravy:
You can put this solution on YOUR website!
=
:
```

row 1 and column 1 signified by r1cl
:
r1c1=2(4)-4(3)=-4
r1c2=2(0)-4(-1)=4
r1c3=2(6)-4(5)=-8
r2c1=0(4)-1(3)=-3
r2c2=0(0)-1(-1)=1
r2c3=0(6)-1(5)=-5
:
```

You can put this solution on YOUR website!
First, we need to find the inverse of the matrix

Solved by pluggable solver: Finding the Inverse of a 2x2 Matrix

To find the inverse of the matrix , we can follow these steps:

### Step 1) Find the determinant

The determinant of is . So this means that

### Step 2) Swap the values

Now switch the highlighted values to get

### Step 3) Change the sign

Now change the sign of the highlighted values to get

### Step 4) Multiply by the inverse of the determinant

Multiply by to get

Plug in to get

### Step 5) Multiply by every element in the matrix (simplify and reduce if possible)

Multiply by EVERY element to get

Multiply to get

Reduce each element:

=================================================================

So the inverse of is

This means that if then

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Now let's use the inverse matrix to find the matrix X:

Left multiply both sides by the inverse

Multiply and to get (this is the identity matrix). Let me know if you need help multiplying matrices.

Multiply and to get .

Multiply the identity matrix (which is I) by X to get

Answer by Edwin McCravy(8999)   (Show Source):
You can put this solution on YOUR website!
Can you help me solve the matrix equation.

```
Method 1:  Using the inverse:

Find the inverse of

Do you know how to find the inverse of a 2x2 matrix?
If not post again asking how.  Or use method 2 below.

The inverse of  is

Left-multiply both sides by this inverse:

-------------------------------

Method 2:  equating corresponding elements:

The right side is a 2x3 matrix.

The 2x2 matrix on the left side must be right

multiplied by a 2x3 matrix to get a 2x3 matrix

Let  be the
required 2x3 matrix. Then, substituting,

(matrix(2,3,a,b,c,d,e,f))

We equate corresponding elements on the 2nd row on both
sides:

, ,

Substituting those:

We equate corresponding elements on the 1st row on both
sides:

So

Edwin```