Use matrices A, B, C, and D to find the following. A=[ 5 7 -1 6 3 -9 ] B=[

Name: Problem 34, Chapter 4: Algebra 2
Uploaded: 2020-03-05T03:25:17-08:00
Duration: 1 min 14 s
Channel: Heather Zimmers
Description: Use matrices A, B, C, and D to find the following. A=[ 5 7 -1 6 3 -9 ] B=[ 8 3 5 1 4 4 ] C=[ 0 4 -2 5 7 -1 ] D=[ 6 2 9 0 -3 0 ] C+(1)/(3) D

step 1 In this problem, we're computing C plus one -third of D. And so it's a really good idea to go ah

Question

Use matrices $A, B, C,$ and $D$ to find the following. $$A=\left[\begin{array}{rr}{5} & {7} \\ {-1} & {6} \\ {3} & {-9}\end{array}\right] \quad B=\left[\begin{array}{ll}{8} & {3} \\ {5} & {1} \\ {4} & {4}\end{array}\right] \quad C=\left[\begin{array}{rr}{0} & {4} \\ {-2} & {5} \\ {7} & {-1}\end{array}\right] \quad D=\left[\begin{array}{ll}{6} & {2} \\ {9} & {0} \\ {-3} & {0}\end{array}\right]$$ $C+\frac{1}{3} D$

   Use matrices $A, B, C,$ and $D$ to find the following.
$$A=\left[\begin{array}{rr}{5} & {7} \\ {-1} & {6} \\ {3} & {-9}\end{array}\right] \quad B=\left[\begin{array}{ll}{8} & {3} \\ {5} & {1} \\ {4} & {4}\end{array}\right] \quad C=\left[\begin{array}{rr}{0} & {4} \\ {-2} & {5} \\ {7} & {-1}\end{array}\right] \quad D=\left[\begin{array}{ll}{6} & {2} \\ {9} & {0} \\ {-3} & {0}\end{array}\right]$$
$C+\frac{1}{3} D$

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 4, Problem 34

Instant Answer

Solved by Expert Heather Zimmers

03/05/2020

Step 1

This means we multiply each element in matrix D by 1/3. This gives us the following matrix: $$\frac{1}{3}D=\left[\begin{array}{cc}{2} & {\frac{2}{3}} \\ {3} & {0} \\ {-1} & {0}\end{array}\right]$$ Show more…

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Use matrices $A, B, C,$ and $D$ to find the following. $$A=\left[\begin{array}{rr}{5} & {7} \\ {-1} & {6} \\ {3} & {-9}\end{array}\right] \quad B=\left[\begin{array}{ll}{8} & {3} \\ {5} & {1} \\ {4} & {4}\end{array}\right] \quad C=\left[\begin{array}{rr}{0} & {4} \\ {-2} & {5} \\ {7} & {-1}\end{array}\right] \quad D=\left[\begin{array}{ll}{6} & {2} \\ {9} & {0} \\ {-3} & {0}\end{array}\right]$$ $C+\frac{1}{3} D$

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Key Concepts

Scalar Multiplication

Scalar multiplication is the process of multiplying each entry of a matrix by a constant (scalar). In the context of the problem, multiplying matrix D by 1/3 means that every element in D is scaled by 1/3, which is a necessary step before performing any further operations with the resulting matrix.

Matrix Addition

Matrix addition involves adding two matrices by adding their corresponding entries, provided the matrices have the same dimensions. After performing scalar multiplication on D, the resulting matrix can be added to matrix C by summing each corresponding element to produce a new matrix. This operation is fundamental for combining matrices in linear algebra.

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