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.

$[\begin{matrix} 5 & x + 2 \\ - 6 y & z \end{matrix}] = [\begin{matrix} a & 3 x - 1 \\ 5 y & 9 \end{matrix}]$

Accepted Answer

Hello, everyone. We are asked to solve the following equation for P QR and S we are given by two matrices. The first matrix has a top row of four P plus three, a second row of negative 11 R S. And this is set equal to the other matrix with the first row as Q and three P minus five. In the second row of negative four R seven, we have four answer choices all of which have slightly different values for P QR. And S recall that if our two matrices are the same dimensions, we can set corresponding elements equal to each other. So what this could look like in the top left corner, we have four in the first matrix Q. In the second matrix. Since we are told they are equal, we can say that Q equals four looking to the next element to the right, we have P plus three as the second element of the first row in the first matrix and three P minus five as the second element of the first row. In the second matrix, we are going to set those equal to each other. So P plus three must equal three P minus five. So solving for P I currently have three equals two, P minus five, add five, eight equals two P divided by two, we get that P equals four. So now we know the value of Q and we know the value of P, both of which somehow are four, all right, continuing with my corresponding pieces. The first element of the second row of the first matrix is negative 11 R and this much equal the first element of the second row of the second matrix which is negative four R. So negative 11 R equals negative four R, if I add 11 article sides, I get zero equals seven R which will give me that R equals zero. OK, we have three variables down one to go. The last one, the last element. So the second element in the second row is S and in the second matrix it's seven. So S must equal seven. So P equals four, Q equals four, R equals zero. S equals seven. And that matches the values in answer choice D have a nice day.

Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} 5 & x + 2 \\ - 6 y & z \end{matrix}] = [\begin{matrix} a & 3 x - 1 \\ 5 y & 9 \end{matrix}]$

Key Concepts

Matrix Equality

Solving Systems of Equations

Substitution and Simplification

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