document.write( "Question 1175989: Solve for X in a 2x3 matrix. \r
\n" ); document.write( "\n" ); document.write( "[-4 -4 -2] [9 -3 -6]
\n" ); document.write( "[3 -2 -6] = -5x-2 [8 6 6]\r
\n" ); document.write( "\n" ); document.write( "(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
\n" ); document.write( "which is multiplied by matrix 2 first row : [9 -3 -6] and second row [8 6 6].\r
\n" ); document.write( "\n" ); document.write( "My attempt is below.\r
\n" ); document.write( "\n" ); document.write( "-45x-18 15x+6 30x+12
\n" ); document.write( "-40x-16 -30x-12 -30x-12''.
\n" ); document.write( " \n" ); document.write( "

Algebra.Com's Answer #801827 by math_tutor2020(3817) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "It sounds like you want to solve
\n" ); document.write( "

\r
\n" ); document.write( "\n" ); document.write( "If my assumption is incorrect, and I'm misreading the question, then please let me know. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let
\n" ); document.write( " $\"A+=+%28matrix%282%2C3%2C-4%2C-4%2C-2%2C3%2C-2%2C-6%29%29\"$
\n" ); document.write( "and
\n" ); document.write( " $\"B+=+%28matrix%282%2C3%2C9%2C-3%2C-6%2C8%2C6%2C6%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "We have the equation
\n" ); document.write( " $\"A+=+-5x-2B\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Let's isolate -5x by adding 2B to both sides
\n" ); document.write( " $\"A+=+-5x-2B\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"A%2B2B+=+-5x-2B%2B2B\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"A%2B2B+=+-5x%2B0%2AB\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"A%2B2B+=+-5x%2B0\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"A%2B2B+=+-5x\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"-5x+=+A%2B2B\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Based on the matrix definitions I stated, we know that
\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"A+%2B+2B+=+%28matrix%282%2C3%2C14%2C-10%2C-14%2C19%2C10%2C6%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So,
\n" ); document.write( " $\"-5x+=+A%2B2B\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"-5x+=+%28matrix%282%2C3%2C14%2C-10%2C-14%2C19%2C10%2C6%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-1%2F5%29%2A%28matrix%282%2C3%2C14%2C-10%2C-14%2C19%2C10%2C6%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x+=+-0.2%2A%28matrix%282%2C3%2C14%2C-10%2C-14%2C19%2C10%2C6%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28matrix%282%2C3%2C-2.8%2C+2%2C+2.8%2C+-3.8%2C+-2%2C+-1.2%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "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.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "This matrix has two rows and three columns.
\n" ); document.write( "The first row has the numbers: -2.8, 2, 2.8
\n" ); document.write( "The second row has the numbers: -3.8, -2, -1.2\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "-----------------------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "To check this answer, we'll do the following steps

Multiply every entry in matrix X by -5. This computes the expression -5X. Let's call this result matrix C.
Multiply every entry in the matrix B by 2. We'll call this result matrix D.
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:
\n" ); document.write( " $\"A+=+%28matrix%282%2C3%2C-4%2C-4%2C-2%2C3%2C-2%2C-6%29%29\"$ (note how A = E)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"B+=+%28matrix%282%2C3%2C9%2C-3%2C-6%2C8%2C6%2C6%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"C+=+%28matrix%282%2C3%2C14%2C-10%2C-14%2C19%2C10%2C6%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"D+=+%28matrix%282%2C3%2C18%2C-6%2C-12%2C16%2C12%2C12%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"E+=+%28matrix%282%2C3%2C-4%2C-4%2C-2%2C3%2C-2%2C-6%29%29\"$ (note how A = E)\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"X+=+%28matrix%282%2C3%2C-2.8%2C+2%2C+2.8%2C+-3.8%2C+-2%2C+-1.2%29%29\"$ \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "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. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Side notes:
\n" ); document.write( "-2.8 = -14/5
\n" ); document.write( "-3.8 = -19/5
\n" ); document.write( "-1.2 = -6/5
\n" ); document.write( "
\n" ); document.write( " \n" ); document.write( "

\n" );