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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 13
Chapter 6, Problem 13

Find the values of the variables for which each statement is true, if possible.
[−3ab5]=[c04d]\(\left\)[ \(\begin{matrix}\) -3 & a \\ b & 5 \(\end{matrix}\) \(\right\)] = \(\left\)[ \(\begin{matrix}\) c & 0 \\ 4 & d \(\end{matrix}\) \(\right\)]

Verified step by step guidance
1
First, carefully read the problem statement to identify the given equations or expressions involving the variables. Since the problem references Examples 1 and 2, review those examples to understand the type of equations or statements you need to solve.
Next, write down the equations or inequalities explicitly. For example, if the problem involves solving for variables in an equation like $ax + b = c$, write it clearly in LaTeX format.
Then, isolate the variable you want to solve for by performing algebraic operations such as addition, subtraction, multiplication, division, or factoring. Remember to apply the same operation to both sides of the equation to maintain equality.
After isolating the variable, simplify the expression as much as possible. This might involve combining like terms, reducing fractions, or applying inverse operations.
Finally, check your solution by substituting the found value(s) back into the original equation(s) to verify that the statements are true. If the substitution holds true, the solution is valid; if not, reconsider the steps or determine if no solution exists.

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Key Concepts

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

Solving Algebraic Equations

This involves finding the values of variables that make an equation true. Techniques include isolating the variable using inverse operations such as addition, subtraction, multiplication, division, and applying properties of equality.
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Introduction to Algebraic Expressions

Understanding Variables and Expressions

Variables represent unknown values in algebraic expressions or equations. Recognizing how to manipulate expressions involving variables is essential to simplify and solve equations accurately.
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Radical Expressions with Variables

Checking Solutions

After finding potential solutions, substituting them back into the original equation verifies their validity. This step ensures that the solutions satisfy the given statements and helps identify extraneous or invalid answers.
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Restrictions on Rational Equations
Related Practice
Textbook Question

Write the augmented matrix for each system and give its dimension. Do not solve.

2x + y + z - 3 = 0

3x - 4y + 2z + 7 = 0

x + y + z - 2 = 0

1
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Textbook Question

Find the partial fraction decomposition for each rational expression. See Examples 1–4. 4/(x(1 - x))

Textbook Question

Evaluate each determinant.

∣345−2∣\(\left\)| \(\begin{matrix}\) 3 & 4 \\ 5 & -2 \(\end{matrix}\) \(\right\)|

4
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Textbook Question

Find the dimension of each matrix. Identify any square, column, or row matrices. See the discussion preceding Example 1.

∣−9∣\(\begin{vmatrix}\)-9\(\end{vmatrix}\)

Textbook Question

Find the dimension of each matrix. Identify any square, column, or row matrices.

[24]\(\left\)[ \(\begin{matrix}\) 2 \\ 4 \(\end{matrix}\) \(\right\)]

Textbook Question

Are the given matrices inverses of each other? (Hint: Check to see whether their products are the identity matrix In.)

[01000−21−10]and[1011000−10]\(\left\)[ \(\begin{matrix}\) 0 & 1 & 0 \\ 0 & 0 & -2 \\ 1 & -1 & 0 \(\end{matrix}\) \(\right\)] \(\quad\) \(\text{and}\) \(\quad\) \(\left\)[ \(\begin{matrix}\) 1 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & -1 & 0 \(\end{matrix}\) \(\right\)]