Find each sum or difference, if possible.

Question

[\begin{matrix} \sqrt{3} & - 4 \\ 2 & - \sqrt{5} \\ - 8 & \sqrt{8} \end{matrix}] - [\begin{matrix} 2 \sqrt{3} & 9 \\ - 2 & \sqrt{5} \\ - 7 & 3 \sqrt{2} \end{matrix}]

Accepted Answer

Hello, everyone. We are asked to calculate the difference for the given matrices. If possible, we are given two matrices. They are both three by two matrices and we are subtracting them. The top row of the first matrix is negative 42 radical three. The second row is radical 65. The third row is two radical 79. The second matrix, the top row is five radical 27. The second row is negative three radical 63, third row is radical 71. We have four answer choices three matrices. And D says the difference does not exist recall that when we subtract or add matrices, they have to have the same dimensions. In this case, both are three by two matrices. So since they have the same dimensions, we can do the subtraction. When we subtract, we are gonna match the corresponding elements and subtract them. So starting in the top left corner, we will have negative four minus five going horizontally. I would have two radical three minus radical 27 which I recall is the same as three radical three. In the second row, we have radical six minus a negative three radical six. The second element of the second row, we'd have five minus three. The first element of the third row, we have two radical seven minus radical seven and the second element of the third row would be nine minus one. So now that I've matched them up, I'm going to do the subtraction, our answer will still be a three by two matrix. So in the top right, I'm sorry, the top left corner four minus five is negative nine, two radical three minus three radical three is a negative radical three. The first element of the second row, um double negatives are like adding. So this is like one radical six plus three radical six. So that would give us four radical six. Second element of the second row would be three minus five is two. The first element of the third row, two radical seven minus radical seven would leave us with one radical seven which is the same as radical seven. And then the second element of the third row nine minus one is eight. So our solution is again a three by two matrix. The top row is negative nine, negative radical three. The second row is four radical 62. The third row is radical 78. And when I go to match those up, it looks like it matches answer choice B have a nice day.

Find each sum or difference, if possible.
$[\begin{matrix} \sqrt{3} & - 4 \\ 2 & - \sqrt{5} \\ - 8 & \sqrt{8} \end{matrix}] - [\begin{matrix} 2 \sqrt{3} & 9 \\ - 2 & \sqrt{5} \\ - 7 & 3 \sqrt{2} \end{matrix}]$

Key Concepts

Matrix Dimensions and Compatibility

Matrix Addition and Subtraction

Representation and Notation of Matrices

Watch next