+0  
 
0
123
3
avatar+794 

If w, x, y, and z are real numbers satisfying:\(\begin{align*} w+x+y &= -2, \\ w+x+z &= 4, \\ w+y+z &= 19, \text{ and} \\ x+y+z &= 12, \end{align*}\)

what is wx + yz?

 Jul 11, 2020
 #1
avatar
0

Matrix system:

\(\begin{pmatrix} 1 & 1 & 1 & 0 \\ 1 & 1 & 0 & 1 \\ 1 & 0 & 1 & 1 \\ 0 & 1 & 1 & 1 \end{pmatrix} \begin{pmatrix} w \\ x \\ y \\ z \end{pmatrix} = \begin{pmatrix} -2 \\ 4 \\ 19 \\ 12 \end{pmatrix} \)

 

Inverting the matrix leads to w = -1, x = -9, y = 6, z = 12, so wx + yz = 63.

 Jul 11, 2020
 #2
avatar+31340 
+1

Hmm.  Check:  If   w = -1, x = -9, y = 6, z = 12,  then w+x+y = -1 - 9 + 6 = 4 not -2.  I think Guest made a mistake in inverting the matrix.

 

Here's the correct matrix inversion:

 

 Jul 12, 2020
 #3
avatar+794 
-1

Thanks!

AnimalMaster  Jul 12, 2020

33 Online Users

avatar
avatar
avatar
avatar