Q13E If possible, compute the matrix ... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 2: Q13E (page 85)

If possible, compute the matrix products in Exercises 1 through 13, using paper and pencil.
13. $[\begin{matrix} 0 & 0 & 1 \end{matrix}] [\begin{matrix} a & b & c \\ d & e & f \\ g & h & k \end{matrix}] [\begin{array}{l} 0 \\ 1 \\ 0 \end{array}]$

Short Answer

Expert verified

Product of given matrix is. $[h]$

Step by step solution

Step1:Matrix multiplication

If A is matrix of order $n 脳 p$ and B is matrix of order $m 脳 q$ . Then the matrix multiplication of $A B$ Is defined only if. $p = m$

If Bis a $m 脳 q$ matrix and A $n 脳 p$ matrix, then the product BAis defined as the matrix of the linear transformation. $T (\overset{鈫�}{x}) = B (A \overset{鈫�}{x})$

Assuming the matrix

Let the given matrix

$A = [\begin{matrix} 0 & 0 & 1 \end{matrix}], B = [\begin{matrix} a & b & c \\ d & e & f \\ g & h & k \end{matrix}], C = [\begin{array}{l} 0 \\ 1 \\ 0 \end{array}]$

Order of Matrix $A$ is $1 脳 3$ , and order of matrix $B$ is, $3 脳 3$ and order of matrix $B$ is $3 脳 1$ .

Multiplication of matrix

First of all we will multiply A and B.

$\begin{matrix} A B = [\begin{matrix} 0 & 0 & 1 \end{matrix}] [\begin{matrix} a & b & c \\ d & e & f \\ g & h & k \end{matrix}] \\ = [\begin{matrix} 0 鈰� a + 0 鈰� d + 1 鈰� g & 0 鈰� b + 0 鈰� e + 1 鈰� h & 0 鈰� c + 0 鈰� f + 1 鈰� k \end{matrix}] \\ = [\begin{matrix} g & h & k \end{matrix}] \end{matrix}$

Now we multiply the product of AB with C.

\begin{matrix} A B C = [\begin{matrix} g & h & k \end{matrix}] [\begin{array}{l} 0 \\ 1 \\ 0 \end{array}] \\ = [g 鈰� 0 + h 鈰� 1 + k 鈰� 0] \\ = [h] \end{matrix}

Hence, the product of given matrix is . $[h]$

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91影视

If possible, compute the matrix products in Exercises 1 through 13, using paper and pencil.
13. $[\begin{matrix} 0 & 0 & 1 \end{matrix}] [\begin{matrix} a & b & c \\ d & e & f \\ g & h & k \end{matrix}] [\begin{array}{l} 0 \\ 1 \\ 0 \end{array}]$

Short Answer

Step by step solution

Step1:Matrix multiplication

Assuming the matrix

Multiplication of matrix

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91影视

If possible, compute the matrix products in Exercises 1 through 13, using paper and pencil.13.[001][abcdefghk][010]

Short Answer

Step by step solution

Step1:Matrix multiplication

Assuming the matrix

Multiplication of matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Theoretical and Mathematical Physics

Decision Maths

Geometry

Calculus

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

If possible, compute the matrix products in Exercises 1 through 13, using paper and pencil.
13. $[\begin{matrix} 0 & 0 & 1 \end{matrix}] [\begin{matrix} a & b & c \\ d & e & f \\ g & h & k \end{matrix}] [\begin{array}{l} 0 \\ 1 \\ 0 \end{array}]$