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Ch. 5 - Systems and Matrices
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 5 - Systems and MatricesProblem 40
Chapter 6, Problem 40

Find each sum or difference, if possible. See Examples 2 and 3.
Two 4x2 matrices with algebraic expressions being subtracted, involving variables and coefficients.

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1
Identify the dimensions of both matrices to ensure they are the same. Since both are 1x4 matrices, they can be added or subtracted element-wise.
Write down the two matrices explicitly, for example, let the first matrix be \(A = \begin{bmatrix} a_1 & a_2 & a_3 & a_4 \end{bmatrix}\) and the second matrix be \(B = \begin{bmatrix} b_1 & b_2 & b_3 & b_4 \end{bmatrix}\).
To find the difference \(A - B\), subtract corresponding elements from each matrix: \(A - B = \begin{bmatrix} a_1 - b_1 & a_2 - b_2 & a_3 - b_3 & a_4 - b_4 \end{bmatrix}\).
Perform the subtraction for each pair of elements to get the resulting 1x4 matrix.
Write the final matrix as the answer, ensuring each element is the difference of the corresponding elements from the original matrices.

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Key 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 1x4, so they are compatible for addition or subtraction.
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Matrix Addition and Subtraction

Matrix addition or subtraction is done by adding or subtracting corresponding elements from each matrix. For example, subtracting two 1x4 matrices involves subtracting each element in the second matrix from the corresponding element in the first matrix, resulting in another 1x4 matrix.
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Element-wise Operations

Element-wise operations mean performing arithmetic on each pair of corresponding elements independently. This concept is fundamental in matrix addition and subtraction, ensuring that each element in the resulting matrix is computed from the elements in the same position in the original matrices.
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Related Practice
Textbook Question

Determine the system of equations illustrated in each graph. Write equations in standard form.

Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components.

3x2 - y2 = 11

xy = 12

Textbook Question

Graph the solution set of each system of inequalities.

3x + 5y ≤ 15

x2 + y2 < 9

Textbook Question

Graph the solution set of each system of inequalities.

2x + y > 2

x - 3y < 6

Textbook Question

Let A=[−2403]A = \(\left\)[ \(\begin{matrix}\) -2 & 4 \\ 0 & 3 \(\end{matrix}\) \(\right\)] and B=[−6240]B = \(\left\)[ \(\begin{matrix}\) -6 & 2 \\ 4 & 0 \(\end{matrix}\) \(\right\)]. Find each of the following.

2A

Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. (4x2 - 3x - 4)/(x3 + x2 - 2x)