Find each product, if possible. [−2−3−42−104−23][01412−132−2]\left[ \begin{matrix} -2 & -3 & -4 \\ 2 & -1 & 0 \\ 4 & -2 & 3 \end{matrix} \right] \left[ \begin{matrix} 0 & 1 & 4 \\ 1 & 2 & -1 \\ 3 & 2 & -2 \end{matrix} \right]

Ch. 5 - Systems and Matrices

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

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Lial 13th Edition

Ch. 5 - Systems and Matrices

Problem 67

Chapter 6, Problem 67

Find each product, if possible.
$[\begin{matrix} - 2 & - 3 & - 4 \\ 2 & - 1 & 0 \\ 4 & - 2 & 3 \end{matrix}] [\begin{matrix} 0 & 1 & 4 \\ 1 & 2 & - 1 \\ 3 & 2 & - 2 \end{matrix}]$

Verified step by step guidance

Identify the expressions or polynomials that need to be multiplied. This could be binomials, trinomials, or other polynomial forms.

Apply the distributive property (also known as the FOIL method for binomials) to multiply each term in the first polynomial by each term in the second polynomial. For example, if multiplying $(a + b)(c + d)$, multiply $a$ by $c$ and $d$, then multiply $b$ by $c$ and $d$.

Write down all the products obtained from the distribution step, ensuring no terms are missed.

Combine like terms by adding or subtracting coefficients of terms with the same variable and exponent to simplify the expression.

Check your final expression to confirm that all terms are combined correctly and that the product is fully simplified.

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Key Concepts

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

Polynomial Multiplication

Polynomial multiplication involves multiplying two or more polynomials by applying the distributive property. Each term in the first polynomial is multiplied by every term in the second polynomial, and like terms are combined to simplify the result.

Distributive Property

The distributive property states that a(b + c) = ab + ac. This property is essential in algebra for expanding expressions and multiplying polynomials by distributing each term across the sum inside parentheses.

Combining Like Terms

After multiplying polynomials, like terms—terms with the same variable raised to the same power—must be combined by adding or subtracting their coefficients to simplify the expression into standard form.

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Combinations

Related Practice

Textbook Question

Graph the solution set of each system of inequalities.

$e^{x}-y$\le$1$

$x-2y$\ge$4$

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Textbook Question

Solve each system. (Hint: In Exercises 69–72, let 1/x = t and 1/y = u.)

2/x + 1/y = 3/2

3/x - 1/y = 1

Textbook Question

Given $A = [\begin{matrix} 4 & - 2 \\ 3 & 1 \end{matrix}],$ and $C = $\left$[ $\begin{matrix}$ -5 & 4 & 1 \\ 0 & 3 & 6 $\end{matrix}$ $\right$]$ , find each product, if possible. See Examples 5–7. BA

Textbook Question

Solve each problem. Find the radius and height (to the nearest thousandth) of an open-ended cylinder with volume 50 in.³ and lateral surface area 65 in.².

Textbook Question

Graph the solution set of each system of inequalities.

$y \leq \log x$

$y \geq ∣ x - 2 ∣$

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Textbook Question

Use Cramer's rule to solve each system of equations. If D = 0, then use another method to determine the solution set. See Examples 5–7.

$5 x + 4 y = 10$

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Find each product, if possible. [−2−3−42−104−23][01412−132−2]\(\left\)[ \(\begin{matrix}\) -2 & -3 & -4 \\ 2 & -1 & 0 \\ 4 & -2 & 3 \(\end{matrix}\) \(\right\)] \(\left\)[ \(\begin{matrix}\) 0 & 1 & 4 \\ 1 & 2 & -1 \\ 3 & 2 & -2 \(\end{matrix}\) \(\right\)]

Verified video answer for a similar problem:

Key Concepts

Polynomial Multiplication

Distributive Property

Combining Like Terms

Find each product, if possible.
$[\begin{matrix} - 2 & - 3 & - 4 \\ 2 & - 1 & 0 \\ 4 & - 2 & 3 \end{matrix}] [\begin{matrix} 0 & 1 & 4 \\ 1 & 2 & - 1 \\ 3 & 2 & - 2 \end{matrix}]$