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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 46
Chapter 6, Problem 46

Let Matrix A displayed as a 2x2 matrix with elements: -2, 4 in the first row; 0, 3 in the second row. and . Find each of the following. See Examples 2 –4.
2A + 4B

Verified step by step guidance
1
Identify the matrices A and B given in the problem. Since the problem statement is incomplete, ensure you have the correct matrices before proceeding.
Multiply matrix A by the scalar 2. This means multiplying every element of matrix A by 2, resulting in the matrix 2A.
Multiply matrix B by the scalar 4. This means multiplying every element of matrix B by 4, resulting in the matrix 4B.
Add the resulting matrices 2A and 4B together. To do this, add corresponding elements from 2A and 4B to form the matrix 2A + 4B.
Write the final matrix 2A + 4B by combining the sums from the previous step, ensuring the dimensions of A and B are the same to perform the addition.

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Key Concepts

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

Matrix Addition and Scalar Multiplication

Matrix addition involves adding corresponding elements of two matrices of the same dimensions. Scalar multiplication means multiplying every element of a matrix by a constant (scalar). Understanding these operations is essential to compute expressions like 2A + 4B.
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Matrix Dimensions and Compatibility

For matrix addition or subtraction, the matrices must have the same dimensions (same number of rows and columns). Ensuring matrices A and B are compatible is crucial before performing operations like 2A + 4B.
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Order of Operations in Matrix Expressions

When evaluating expressions like 2A + 4B, scalar multiplication is performed first on each matrix, followed by matrix addition. This order ensures accurate computation of the resulting matrix.
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Related Practice
Textbook Question

Let and . Find each of the following. See Examples 2 –4.

(3/2)B

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Textbook Question

Graph the solution set of each system of inequalities. x + 2y ≤ 4 y ≥ x2 - 1

587
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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.

-A + (1/2)B

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Textbook Question

Graph the solution set of each system of inequalities.

4x - 3y ≤ 12

y ≤ x2

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Textbook Question

Use the determinant theorems to evaluate each determinant.

∣68−12−10240−8∣\(\left\)| \(\begin{matrix}\) 6 & 8 & -12 \\ -1 & 0 & 2 \\ 4 & 0 & -8 \(\end{matrix}\) \(\right\)|

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Textbook Question

Solve each equation. ∣3x7−x4∣=8\(\left\)| \(\begin{matrix}\) 3x & 7 \\ -x & 4 \(\end{matrix}\) \(\right\)| = 8

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