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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 12c
Chapter 7, Problem 12c

In Exercises 9 - 16, find the following matrices: c. - 4A
Matrices A and B for college algebra, chapter 7, introduction to matrices.

Verified step by step guidance
1
Identify matrix A as \( A = \begin{bmatrix} 3 & 1 & 1 \\ -1 & 2 & 5 \end{bmatrix} \).
Understand that the problem asks to find \( -4A \), which means multiplying every element of matrix A by -4.
Multiply each element of matrix A by -4: for example, multiply 3 by -4, 1 by -4, and so on for all elements.
Write the resulting matrix after multiplication, keeping the same dimensions as matrix A.
Verify that each element in the new matrix is correctly calculated as \( -4 \times \text{original element} \).

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Key Concepts

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

Matrix Scalar Multiplication

Scalar multiplication involves multiplying every element of a matrix by a constant (scalar). For example, multiplying matrix A by -4 means each entry in A is multiplied by -4, resulting in a new matrix with scaled values.
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Matrix Representation and Notation

A matrix is a rectangular array of numbers arranged in rows and columns, denoted by brackets. Understanding how to read and write matrices, such as A and B given here, is essential for performing operations like addition, subtraction, and scalar multiplication.
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Element-wise Operations on Matrices

Matrix operations like addition, subtraction, and scalar multiplication are performed element-wise. This means each corresponding element in the matrix is operated on individually, which is crucial for correctly computing expressions like -4A.
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Related Practice
Textbook Question

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

Textbook Question

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

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Textbook Question

Use the fact that if A=[abcd]A = \(\begin{bmatrix}\) a & b \\ c & d \(\end{bmatrix}\), then A−1=1ad−bc[d−b−ca]A^{-1} = \(\frac{1}{ad-bc}\) \(\begin{bmatrix}\) d & -b \\ -c & a \(\end{bmatrix}\) to find the inverse of each matrix, if possible. Check that AA−1=I2AA^{-1} = I_2 and A−1A=I2A^{-1} A = I_2.

A=[23−12]A = \(\begin{bmatrix}\) 2 & 3 \\ -1 & 2 \(\end{bmatrix}\)

Textbook Question

Find the following matrices: - 3A + 2B

A=[311−125],B=[2−36−31−4]A = \(\begin{bmatrix}\)3 & 1 & 1 \\-1 & 2 & 5\(\end{bmatrix}\), B = \(\begin{bmatrix}\)2 & -3 & 6 \\-3 & 1 & -4\(\end{bmatrix}\)

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Textbook Question

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

Textbook Question

Perform each matrix row operation and write the new matrix.

[2−64∣1015−5∣0304∣7]12R1\(\begin{bmatrix}\)2 & -6 & 4 & \(\vert\) & 10 \\1 & 5 & -5 & \(\vert\) & 0 \\3 & 0 & 4 & \(\vert\) & 7\(\end{bmatrix}\]\quad\) \(\frac{1}{2}\)R_1

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