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.

$[\begin{matrix} - 3 & a \\ b & 5 \end{matrix}] = [\begin{matrix} c & 0 \\ 4 & d \end{matrix}]$

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 two by two matrix where the first row is negative five Q. The second row is R negative two and that's equal to a two by two matrix where the first row is P negative one. And the second row is eight S. Our answer choices are A P equals negative five, Q equals negative one, R equals negative two. S equals eight B P equals negative one, Q equals negative five, R equals negative two. S equals eight C P equals negative five, Q equals negative one, R equals eight S equals negative two D P equals negative one. Q equals negative five, R equals eight S equals negative two. If we are to assume that these are equal because the statement we are given says they are equal, we can match up the locations within the matrices to find the values. So I'm rewriting this. So again, my top row was negative five, Q second row was R negative two and that equals the matrix P negative one for the first row. Eight S for the second row. So matching these up P is in the top left corner of the second matrix. The value that's in the top left corner of the first matrix is negative five. So P should equal negative five. Next, looking at Q Q is in the top right corner of the first matrix. The value that's in the top right corner of the second matrix is negative one. So Q should equal negative one. R is in the bottom left corner of the first matrix and it matches eight which is in the bottom left corner of the second matrix. So R equals eight and that leaves us with S which is in the bottom right corner of the second matrix negative two is in the bottom right corner of the first matrix. So S should equal negative two. These are our values with what they equal, finding the right answer choice. Make sure you check your signs and that you've matched up the right letter. So P equals negative five, Q equals negative one. Um R equals eight S equals negative two. So that is answer choice. C have a nice day.

Find the values of the variables for which each statement is true, if possible.
$[\begin{matrix} - 3 & a \\ b & 5 \end{matrix}] = [\begin{matrix} c & 0 \\ 4 & d \end{matrix}]$

Key Concepts

Solving Algebraic Equations

Understanding Variables and Expressions

Checking Solutions

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