SOLUTION: Hi. I am really struggling to answer a certain matrix problem and I am unable to find examples of this type on my own. I attempted to multiple the 4x+3 to each number and setting

Algebra ->  Matrices-and-determiminant -> SOLUTION: Hi. I am really struggling to answer a certain matrix problem and I am unable to find examples of this type on my own. I attempted to multiple the 4x+3 to each number and setting      Log On


   

Question 825491: Hi. I am really struggling to answer a certain matrix problem and I am unable to find examples of this type on my own. I attempted to multiple the 4x+3 to each number and setting it equal to the corresponding number, but I kept getting a ton of fractions that did not seem right. Also the 3,3,1, and -2 are one matrix and 10,8,5, and -2 are the other but it won't line up correctly.
4x+3[ 3 2 ] = [ 10 8]
[ 1 -2 ] [ 5 -2 ]
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
(First of all, algebra.com uses large parentheses, ( and ), around matrices instead of the more common large brackets, [ and ]. Keep this in mind as we go through the problem.)

The fractions you got are not by themselves a sign of an error. The problems you are experiencing are due to the fact that you are misunderstanding the equation. It is not

Instead it is:

The important differences are:
  • The first matrix is only multiplied by 3, not 4x+3.
  • The "x" is a matrix, not a number.
Now let's solve for the matrix "x". Multiplying the first matrix by 3 we get:

Subtracting the matrix on the left from both sides we get:

which simplifies to:
4x+=+%28matrix%282%2C+2%2C+1%2C+2%2C+2%2C+4%29%29
Multiplying both sides by 1/4:
x+=+%281%2F4%29%2A%28matrix%282%2C+2%2C+1%2C+2%2C+2%2C+4%29%29
which simplifies to:
x+=+%28matrix%282%2C+2%2C+1%2F4%2C+1%2F2%2C+1%2F2%2C+1%29%29
This is the solution.