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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 15a
Chapter 7, Problem 15a

In Exercises 9 - 16, find the following matrices: a. A + B
Matrices A and B for exercise 15 in college algebra, chapter on matrices and determinants.

Verified step by step guidance
1
Step 1: Understand that to find the sum of two matrices A and B, both matrices must have the same dimensions. Here, both A and B are 3x3 matrices, so addition is possible.
Step 2: Recall that matrix addition is performed by adding corresponding elements from each matrix. That is, if A = [a_ij] and B = [b_ij], then A + B = [a_ij + b_ij].
Step 3: Write down the elements of matrices A and B clearly: A = \(\begin{bmatrix}\) 2 & -10 & -2 \\ 14 & 12 & 10 \\ 4 & -2 & 2 \(\end{bmatrix}\), B = \(\begin{bmatrix}\) 6 & 10 & -2 \\ 0 & -12 & -4 \\ -5 & 2 & -2 \(\end{bmatrix}\)
Step 4: Add each corresponding element: - For the element in the first row, first column: 2 + 6 - For the element in the first row, second column: -10 + 10 - Continue this process for all elements in the matrices.
Step 5: After adding all corresponding elements, write the resulting matrix as the sum A + B.

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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

Matrix dimensions are expressed as rows × columns and determine the size of a matrix. For matrix addition, both matrices must have identical dimensions to ensure each element pairs correctly. Understanding dimensions helps verify if operations like addition or multiplication are valid.
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Element-wise Operations

Element-wise operations apply a mathematical operation to each corresponding element of matrices. In addition, subtraction, or scalar multiplication, each element is treated independently. This concept is fundamental for performing matrix addition accurately.
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