Answered: 4 5 A = B = c = -3 C = -2 -2 1_

PREALGEBRA

15th Edition

ISBN:9781938168994

Author:OpenStax

Publisher:OpenStax

Chapter10: Polynomials

Section10.1: Add And Subtract Polynomials

Problem 10.15TI: Subtract: (4n27n3)from (8n2+5n3).

See similar textbooks

Related questions

Question

Perform the indicated matrix operation A(B + C) given that A, B, and C are defined as shown attached. If an operation is not defined, state the reason.

Expert Solution

Step 1

Consider the matrix

$A = [\begin{matrix} 4 \\ - 3 \\ 0 \end{matrix} \begin{matrix} 0 \\ 5 \\ 1 \end{matrix}], B = [\begin{matrix} 5 & 1 \\ - 2 & - 2 \end{matrix}] C = [\begin{matrix} 1 & - 1 \\ - 1 & 1 \end{matrix}]$

Step 2

$\begin{array}{l} A (B + C) = [\begin{matrix} 4 \\ - 3 \\ 0 \end{matrix} \begin{matrix} 0 \\ 5 \\ 1 \end{matrix}] ([\begin{matrix} 5 & 1 \\ - 2 & - 2 \end{matrix}] + [\begin{matrix} 1 & - 1 \\ - 1 & 1 \end{matrix}]) \\ = [\begin{matrix} 4 \\ - 3 \\ 0 \end{matrix} \begin{matrix} 0 \\ 5 \\ 1 \end{matrix}] ([\begin{matrix} 5 + 1 & 1 - 1 \\ - 2 - 1 & - 2 + 1 \end{matrix}]) (Componentwise addition) \\ = [\begin{matrix} 4 \\ - 3 \\ 0 \end{matrix} \begin{matrix} 0 \\ 5 \\ 1 \end{matrix}] ([\begin{matrix} 6 & 0 \\ - 3 & - 1 \end{matrix}]) \\ = [\begin{matrix} 4 \\ - 3 \\ 0 \end{matrix} \begin{matrix} 0 \\ 5 \\ 1 \end{matrix}] [\begin{matrix} 6 & 0 \\ - 3 & - 1 \end{matrix}] \end{array}$

Now multiplication is possible because Matrix is of orders $3 \times 2 a n d 2 \times 2$

$\begin{array}{l} = [\begin{matrix} 4 \times 6 + 0 \times (- 3) \\ - 3 \times 6 + 5 \times (- 3) \\ 0 \times 6 + 1 \times (- 3) \end{matrix} \begin{matrix} 4 \times 0 + 0 \times (- 1) \\ - 3 \times 0 + 5 \times (- 1) \\ 0 \times 0 + 1 \times (- 1) \end{matrix}] \\ = [\begin{matrix} 24 \\ - 33 \\ - 3 \end{matrix} \begin{matrix} 0 \\ - 5 \\ - 1 \end{matrix}] \\ A (B + C) = [\begin{matrix} 24 \\ - 33 \\ - 3 \end{matrix} \begin{matrix} 0 \\ - 5 \\ - 1 \end{matrix}] \end{array}$

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

Knowledge Booster

$Complexity$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions