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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 27
Chapter 6, Problem 27

Find each sum or difference, if possible.
[6−92413]+[−8256−34]\(\left\)[ \(\begin{matrix}\) 6 & -9 & 2 \\ 4 & 1 & 3 \(\end{matrix}\) \(\right\)] + \(\left\)[ \(\begin{matrix}\) -8 & 2 & 5 \\ 6 & -3 & 4 \(\end{matrix}\) \(\right\)]

Verified step by step guidance
1
Identify the dimensions of both matrices to ensure they are the same. Since both are 2x3 matrices, addition or subtraction is possible.
Recall that matrix addition (or subtraction) is performed element-wise. This means you add (or subtract) corresponding elements from each matrix.
Write down the general formula for matrix addition: if \(A = [a_{ij}]\) and \(B = [b_{ij}]\), then \(A + B = [a_{ij} + b_{ij}]\) for all \(i\) and \(j\).
Add the corresponding elements from each matrix. For example, add the element in the first row and first column of the first matrix to the element in the first row and first column of the second matrix, and continue this for all elements.
After performing the element-wise addition, write the resulting matrix with the sums in their respective positions to complete the solution.

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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 or subtraction requires both matrices to have the same dimensions, meaning the same number of rows and columns. If the matrices differ in size, their sum or difference is undefined. Understanding this ensures that operations are only performed on compatible matrices.
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Matrix Addition and Subtraction

To add or subtract matrices, you perform the operation element-wise, combining corresponding entries from each matrix. For example, the element in the first row and first column of the result is the sum or difference of the elements in the first row and first column of the original matrices.
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Notation and Representation of Matrices

Matrices are typically represented as rectangular arrays enclosed in brackets, with rows and columns clearly defined. Understanding how to read and write matrices correctly is essential for performing operations and interpreting results in algebra.
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Related Practice
Textbook Question

Solve each system, using the method indicated.

3x + y = -7

x - y = -5 (Gaussian elimination)

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Textbook Question

Solve each nonlinear system of equations. Give all solutions, including those with nonreal complex components. See Examples 1–5.

x2+y2=02x^2+y^2=02

x2−3y2=0x^2-3y^2=0

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Textbook Question

Evaluate each determinant.

∣1−23000110−12∣\(\left\)| \(\begin{matrix}\) 1 & -2 & 3 \\ 0 & 0 & 0 \\ 1 & 10 & -12 \(\end{matrix}\) \(\right\)|

Textbook Question

Solve each system by elimination. In systems with fractions, first clear denominators.

x/2+ y/3 = 4

3x/2+3y/2 = 15

Textbook Question

Find the inverse, if it exists, for each matrix.[22−4260−3−35]\(\left\)[ \(\begin{matrix}\) 2 & 2 & -4 \\2 & 6 & 0 \\-3 & -3 & 5 \(\end{matrix}\) \(\right\)]

Textbook Question

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