SOLUTION: Can anyone help me with these problems please? 1) Use the matrix method to solve: 5x + 3y = 3 2x - 6y = 30 x = ____ y = ____ 2) Perform the following operations on

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Question 202458: Can anyone help me with these problems please?
1) Use the matrix method to solve:
5x + 3y = 3
2x - 6y = 30
x = ____
y = ____

2) Perform the following operations on matrices.
(4) + (8) = (____)
(7) (2) (____)

3) Perform the following operations on matrices.
(1 8)(7 6) = (___ ___)
(0 7)(7 4) (___ ___)

Thank you in advance for all your help.
~Sarah
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
# 1

First, convert the system





into the matrix equation





So what we now need is inverse matrix of to isolate


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:


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


Answer:

So the inverse of is

This means that if then




Now left multiply both sides by the inverse matrix to get






AMP Rendering Error of '(matrix(2,2,1,0,0,1))(matrix(2,1,x,y))=(matrix(2,2,3,-4))'.




AMP Rendering Error of '(matrix(2,1,x,y))=(matrix(2,2,3,-4))'.



So this means that and


Note: let me know if you need help with matrix multiplication.





# 2

Simply add the corresponding components:





So





# 3


Since the first matrix is a 2 by 2 matrix and the second matrix is a 2 by 2 matrix, this means that the resulting matrix will be a 2 by 2 matrix.

So the final resulting matrix will look like:





note: the "x"s are just placeholders for now



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




Multiply the corresponding entries from the 1st row of the first matrix by the 1st column of the second matrix. After multiplying, add the values:


1st row, 1st column:



So the element in the 1st row, 1st column of the resulting matrix is . Now let's update the matrix:


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




Multiply the corresponding entries from the 1st row of the first matrix by the 2nd column of the second matrix. After multiplying, add the values:


1st row, 2nd column:



So the element in the 1st row, 2nd column of the resulting matrix is . Now let's update the matrix:






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




Multiply the corresponding entries from the 2nd row of the first matrix by the 1st column of the second matrix. After multiplying, add the values:


2nd row, 1st column:



So the element in the 2nd row, 1st column of the resulting matrix is . Now let's update the matrix:


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




Multiply the corresponding entries from the 2nd row of the first matrix by the 2nd column of the second matrix. After multiplying, add the values:


2nd row, 2nd column:



So the element in the 2nd row, 2nd column of the resulting matrix is . Now let's update the matrix:










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


Answer:


So the solution is

In other words,


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