Find the values of the variables for which each statement is t...

Question

Find the values of the variables for which each statement is true, if possible.

$[\begin{matrix} 0 & 5 & x \\ - 1 & 3 & y + 2 \\ 4 & 1 & z \end{matrix}] = [\begin{matrix} 0 & w & 6 \\ - 1 & 3 & 0 \\ 4 & 1 & 8 \end{matrix}]$

Accepted Answer

Hello, everyone. We are asked to determine if possible. The values of the variables that satisfy the given statement. The statement we are given is a three by three matrix where the top row is 9 12 P. The second row is negative 14, R plus five. The third row is 85 T and this equals a three by three matrix with the top row nine Q seven, second row negative 14 11. In third row 856, our answer choices are A P equals seven, Q equals six, R equals six T equals B P equals seven, Q equals 12, R equals six, T equals six C P equals 12, Q equals seven, R equals six, T equals six D P equals six. QQ equals 12, R equals six T equals seven. So if the statement we are given our three by three matrices are equal to each other. And that is true, we can match up corresponding elements from both matrices. So starting in the top row of the first matrix, the first variable I come across is P P is in the third spot in the top row. So matching that to the third spot in the top row of the second matrix, I see that P has to equal seven as those correspond continuing across the top row. The second element in the top row of the second matrix is a Q Q must correspond to the second element in the top row of the first matrix which is 12. There's nothing we need to solve. Once we've matched them up, we know their values. The next variable I come across is the third element of the second row of the first matrix. And that's R plus five that needs to equal to the third element of the second row of the second matrix which is 11. So R plus five equals 11 solving for R I subtract five and I get the R equal six. Finally, the last variable is T, it is in the third, I'm sorry. It's the third element in the third row of the first matrix. And so that would equal to the third element of the third row of the second matrix which is six. So now that we've matched them up, we know P equals seven, Q equals 12, R equals six, P equals six, matching that to my answer choices. Uh P equals seven. So it's either A or B Q equals 12, R equals six, T equals six. So that has to be answer choice B that is the only one where all those variables have those values have a nice day.

Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} 0 & 5 & x \\ - 1 & 3 & y + 2 \\ 4 & 1 & z \end{matrix}] = [\begin{matrix} 0 & w & 6 \\ - 1 & 3 & 0 \\ 4 & 1 & 8 \end{matrix}]$

Key Concepts

Solving Equations

Checking for Solutions

Understanding Variable Constraints

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