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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 14b
Chapter 7, Problem 14b

In Exercises 9 - 16, find the following matrices: b. A - B
Matrices A and B for exercise 14 in college algebra, showing A = [6 2 -3] and B = [4 -2 3].

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Step 1: Identify the matrices A and B. Here, A = [6 2 -3] and B = [4 -2 3]. Both are 1x3 matrices (row vectors).
Step 2: Understand that matrix subtraction A - B is performed by subtracting corresponding elements of B from A.
Step 3: Set up the subtraction element-wise: (6 - 4), (2 - (-2)), and (-3 - 3).
Step 4: Perform each subtraction separately: 6 - 4, 2 - (-2), and -3 - 3, but do not calculate the final values yet.
Step 5: Write the resulting matrix as [6 - 4, 2 - (-2), -3 - 3], which represents the matrix A - B.

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Key Concepts

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

Matrix Representation

A matrix is a rectangular array of numbers arranged in rows and columns. In this problem, matrices A and B are 1x3 row matrices, meaning they each have one row and three columns. Understanding the structure of matrices is essential for performing operations like addition or subtraction.
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Matrix Subtraction

Matrix subtraction involves subtracting corresponding elements of two matrices of the same dimensions. For matrices A and B, each element in A is subtracted by the corresponding element in B to form a new matrix. This operation is only defined when both matrices have identical dimensions.
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Element-wise Operations

Element-wise operations apply arithmetic operations to each corresponding element in matrices. For subtraction, this means subtracting each element in matrix B from the corresponding element in matrix A individually. This concept ensures clarity in performing matrix operations correctly.
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