Textbook Question
Let and . Find each of the following. See Examples 2 –4.
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7. Systems of Equations & Matrices
Determinants and Cramer's Rule
2:11 minutesProblem 33
Textbook Question
Find each sum or difference, if possible. See Examples 2 and 3.
![Two vertical 3x1 matrices with elements [12, -1, 3] and [8, 4, -1] separated by a minus sign.](https://static.studychannel-dev.pearsondev.tech/courses/college-algebra/thumbnails/6033cf67-9d5b-4ab3-a80f-23169e3d5e71)
Verified step by step guidance1
Identify the dimensions of the matrices involved. Both matrices are 3x1, meaning they each have 3 rows and 1 column.
Recall that matrix addition or subtraction is only possible when the matrices have the same dimensions. Since both are 3x1, subtraction is possible.
Subtract the corresponding elements of the two matrices. If the first matrix is \( \begin{bmatrix} a_1 \\ a_2 \\ a_3 \end{bmatrix} \) and the second matrix is \( \begin{bmatrix} b_1 \\ b_2 \\ b_3 \end{bmatrix} \), then the difference is \( \begin{bmatrix} a_1 - b_1 \\ a_2 - b_2 \\ a_3 - b_3 \end{bmatrix} \).
Write the resulting matrix by performing the subtraction for each corresponding element.
Verify your result by checking that the resulting matrix still has dimensions 3x1.
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Video duration:
2mKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Matrix Dimensions and Compatibility
Matrix addition and subtraction require the matrices to have the same dimensions. This means both matrices must have the same number of rows and columns to perform element-wise operations. In this question, both matrices are 3x1, so subtraction is possible.
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Matrix Addition and Subtraction
Matrix addition and subtraction involve combining corresponding elements from each matrix. For subtraction, subtract each element of the second matrix from the corresponding element of the first matrix. This operation is done element-wise and results in a matrix of the same size.
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Representation of Matrices
A 3x1 matrix is a column matrix with three rows and one column. Understanding this helps visualize the operation and ensures correct alignment of elements during addition or subtraction. Each element corresponds to a specific position in the matrix.
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