SOLUTION: Solve for X in a 2x3 matrix. [-4 -4 -2] [9 -3 -6] [3 -2 -6] = -5x-2 [8 6 6] (the layout shifts after I press the preview

Algebra ->  Matrices-and-determiminant -> SOLUTION: Solve for X in a 2x3 matrix. [-4 -4 -2] [9 -3 -6] [3 -2 -6] = -5x-2 [8 6 6] (the layout shifts after I press the preview      Log On


   

Question 1175989: Solve for X in a 2x3 matrix.
[-4 -4 -2] [9 -3 -6]
[3 -2 -6] = -5x-2 [8 6 6]
(the layout shifts after I press the preview question, but Matrix 1 first row should be [-4 -4 -2] and second row [3 -2 -6] = -5x-2
which is multiplied by matrix 2 first row : [9 -3 -6] and second row [8 6 6].
My attempt is below.
-45x-18 15x+6 30x+12
-40x-16 -30x-12 -30x-12''.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

It sounds like you want to solve

If my assumption is incorrect, and I'm misreading the question, then please let me know.

Let
A+=+%28matrix%282%2C3%2C-4%2C-4%2C-2%2C3%2C-2%2C-6%29%29
and
B+=+%28matrix%282%2C3%2C9%2C-3%2C-6%2C8%2C6%2C6%29%29

We have the equation
A+=+-5x-2B

Let's isolate -5x by adding 2B to both sides
A+=+-5x-2B

A%2B2B+=+-5x-2B%2B2B

A%2B2B+=+-5x%2B0%2AB

A%2B2B+=+-5x%2B0

A%2B2B+=+-5x

-5x+=+A%2B2B

Based on the matrix definitions I stated, we know that








A+%2B+2B+=+%28matrix%282%2C3%2C14%2C-10%2C-14%2C19%2C10%2C6%29%29

So,
-5x+=+A%2B2B

-5x+=+%28matrix%282%2C3%2C14%2C-10%2C-14%2C19%2C10%2C6%29%29

x+=+%28-1%2F5%29%2A%28matrix%282%2C3%2C14%2C-10%2C-14%2C19%2C10%2C6%29%29

x+=+-0.2%2A%28matrix%282%2C3%2C14%2C-10%2C-14%2C19%2C10%2C6%29%29



x+=+%28matrix%282%2C3%2C-2.8%2C+2%2C+2.8%2C+-3.8%2C+-2%2C+-1.2%29%29

We see that x is a matrix. Convention usually has uppercase letters as the labels of a matrix. This means it is better to use uppercase X instead of lowercase x.

This matrix has two rows and three columns.
The first row has the numbers: -2.8, 2, 2.8
The second row has the numbers: -3.8, -2, -1.2

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

To check this answer, we'll do the following steps
  1. Multiply every entry in matrix X by -5. This computes the expression -5X. Let's call this result matrix C.
  2. Multiply every entry in the matrix B by 2. We'll call this result matrix D.
  3. Subtract the matrices C and D. The order is C-D. You'll pair up each corresponding entry when doing the subtraction. Let's call this result matrix E.
We should have these matrices:
A+=+%28matrix%282%2C3%2C-4%2C-4%2C-2%2C3%2C-2%2C-6%29%29 (note how A = E)

B+=+%28matrix%282%2C3%2C9%2C-3%2C-6%2C8%2C6%2C6%29%29

C+=+%28matrix%282%2C3%2C14%2C-10%2C-14%2C19%2C10%2C6%29%29

D+=+%28matrix%282%2C3%2C18%2C-6%2C-12%2C16%2C12%2C12%29%29

E+=+%28matrix%282%2C3%2C-4%2C-4%2C-2%2C3%2C-2%2C-6%29%29 (note how A = E)

X+=+%28matrix%282%2C3%2C-2.8%2C+2%2C+2.8%2C+-3.8%2C+-2%2C+-1.2%29%29

The entire right hand side of -5X-2B becomes matrix E. Since matrix A and matrix E are the same, this shows that A = E and that leads to A = -5X-2B being true as well. This confirms the answer.

Side notes:
-2.8 = -14/5
-3.8 = -19/5
-1.2 = -6/5