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Ch. 6 - Matrices and Determinants
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 6 - Matrices and DeterminantsProblem 9a
Chapter 7, Problem 9a

In Exercises 9 - 16, find the following matrices: a. A + B
Matrices A and B for exercise 9 in college algebra, chapter on matrices and determinants.

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Step 1: Understand that matrix addition involves adding corresponding elements from each matrix. Both matrices A and B must have the same dimensions, which they do here (2 rows and 2 columns).
Step 2: Write down the matrices clearly: A = \( \begin{bmatrix} 4 & 1 \\ 3 & 2 \end{bmatrix} \), B = \( \begin{bmatrix} 5 & 9 \\ 0 & 7 \end{bmatrix} \).
Step 3: Add the elements in the first row and first column: 4 (from A) + 5 (from B) = 4 + 5.
Step 4: Add the elements in the first row and second column: 1 (from A) + 9 (from B) = 1 + 9.
Step 5: Repeat the process for the second row: 3 + 0 for the first column, and 2 + 7 for the second column.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Matrix Addition

Matrix addition involves adding corresponding elements from two matrices of the same dimensions. Each element in the resulting matrix is the sum of elements in the same position from the original matrices. This operation is only defined when both matrices have the same number of rows and columns.
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Matrix Dimensions

The dimension of a matrix is given by the number of rows and columns it contains, expressed as 'rows × columns'. For matrix addition, both matrices must have identical dimensions to ensure each element corresponds correctly for addition.
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Element-wise Operations

Element-wise operations on matrices, such as addition, require performing the operation on each pair of corresponding elements individually. Understanding this helps in correctly computing the sum of matrices by focusing on each element's position.
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Related Practice
Textbook Question

Find the products AB and BA to determine whether B is the multiplicative inverse of A.

A=[123134143],B=[72−312−12012−121−12]A = \(\begin{bmatrix}\) 1 & 2 & 3 \\ 1 & 3 & 4 \\ 1 & 4 & 3 \(\end{bmatrix}\), \(\quad\) B = \(\begin{bmatrix}\) \(\frac{7}{2}\) & -3 & \(\frac{1}{2}\) \\ -\(\frac{1}{2}\) & 0 & \(\frac{1}{2}\) \\ -\(\frac{1}{2}\) & 1 & -\(\frac{1}{2}\) \(\end{bmatrix}\)

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Textbook Question

In Exercises 9 - 16, find the following matrices: c. - 4A

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Textbook Question

Evaluate each determinant in Exercises 1–10.∣121218−34∣\(\begin{vmatrix}\[\frac{1}{2}\) & \(\frac{1}{2}\) \(\frac{1}{8}\) & - \(\frac{3}{4}\]\end{vmatrix}\)

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Textbook Question

In Exercises 9 - 16, find the following matrices: b. A - B

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Textbook Question

In Exercises 8–11, use Gaussian elimination to find the complete solution to each system, or show that none exists.

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Textbook Question

In Exercises 9 - 16, find the following matrices: d. - 3A + 2B

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