Video Transcript
Evaluate the determinant of the two-by-two matrix three, negative four, one, five.
In this question, we’re asked to evaluate the determinant of a two-by-two matrix. And to do that, we first need to recall what we mean by the determinant of a two-by-two matrix. The determinant of a two-by-two matrix is the difference between the product of the diagonals. In other words, the determinant of the two-by-two matrix 𝑎, 𝑏, 𝑐, 𝑑 is equal to 𝑎𝑑 minus 𝑏𝑐. We take the product of the first diagonal, that’s 𝑎 multiplied by 𝑑, and subtract the product of the other diagonal, that’s 𝑏 multiplied by 𝑐.
We want to use this definition to find the determinant of the two-by-two matrix three, negative four, one, five. First, we need to multiply three by five. Then, we need to subtract one multiplied by negative four. So the determinant of this matrix is three multiplied by five minus one multiplied by negative four. And then we can just evaluate this expression. Three multiplied by five is equal to 15, and then we’re subtracting one multiplied by negative four, which is the same as adding four. Finally, 15 plus four is equal to 19, which is our final answer. Therefore, we were able to show the determinant of the two-by-two matrix three, negative four, one, five is equal to 19.
