+0

# help!

0
79
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+798

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
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
+30920
+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
+798
-1

Thanks!

AnimalMaster  Jul 12, 2020