Q15E Use the given partitions to comp... [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: Q15E (page 85)

Use the given partitions to compute the products in Exercises 15 and 16. Check your work by computing the same products without using a partition. Show all your work.
15. $[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 3 & 4 \end{matrix}] [\begin{matrix} 1 & 0 \\ 2 & 0 \\ 3 & 4 \end{matrix}]$

Short Answer

Expert verified

The product is $[\begin{matrix} 1 & 0 \\ 2 & 0 \\ 19 & 16 \end{matrix}]$ . $[\begin{matrix} 1 & 0 \\ 2 & 0 \\ 19 & 16 \end{matrix}]$

Step by step solution

Block matrix

Let the given matrix. $A = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 3 & 4 \end{matrix}], B = [\begin{matrix} 1 & 0 \\ 2 & 0 \\ 3 & 4 \end{matrix}]$

In the blocking format given matrix can be written as

$A = [\begin{matrix} A_{11} & A_{12} \\ A_{21} & A_{22} \end{matrix}], B = [\begin{matrix} B_{11} & B_{12} \\ B_{21} & B_{22} \end{matrix}],$

Multiplication of block matrix

Multiplication of block matrix is done like as follows.

$\begin{array}{l} A B = [\begin{matrix} [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] [\begin{matrix} 1 \\ 2 \end{matrix}] + [\begin{array}{l} 0 \\ 0 \end{array}] [3] & [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}] [\begin{array}{l} 0 \\ 0 \end{array}] + [\begin{array}{l} 0 \\ 0 \end{array}] [4] \\ [\begin{matrix} 1 & 3 \end{matrix}] [\begin{array}{l} 1 \\ 2 \end{array}] + [4] [3] & [\begin{matrix} 1 & 3 \end{matrix}] [\begin{array}{l} 0 \\ 0 \end{array}] + [4] [3] \end{matrix}] \\ A B = [\begin{matrix} [\begin{array}{l} 1 \\ 2 \end{array}] + [\begin{array}{l} 0 \\ 0 \end{array}] & [\begin{array}{l} 0 \\ 0 \end{array}] + [\begin{array}{l} 0 \\ 0 \end{array}] \\ [7] + [12] & [16] \end{matrix}] \\ A B = [\begin{matrix} \begin{array}{l} 1 \\ 2 \end{array} & \begin{array}{l} 0 \\ 0 \end{array} \\ 19 & 16 \end{matrix}] \end{array}$

Checking the product

Here, we will check the product by doing simple multiplication.

$\begin{matrix} A B = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 3 & 4 \end{matrix}] [\begin{matrix} 1 & 0 \\ 2 & 0 \\ 3 & 4 \end{matrix}] \\ = [\begin{matrix} 1 & 0 \\ 2 & 0 \\ 19 & 16 \end{matrix}] \end{matrix}$

Hence, the product is.localid="1664881137586" $[\begin{matrix} 1 & 0 \\ 2 & 0 \\ 19 & 16 \end{matrix}]$

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91影视

Use the given partitions to compute the products in Exercises 15 and 16. Check your work by computing the same products without using a partition. Show all your work.
15. $[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 3 & 4 \end{matrix}] [\begin{matrix} 1 & 0 \\ 2 & 0 \\ 3 & 4 \end{matrix}]$

Short Answer

Step by step solution

Block matrix

Multiplication of block matrix

Checking the product

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Discrete Mathematics

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91影视

Use the given partitions to compute the products in Exercises 15 and 16. Check your work by computing the same products without using a partition. Show all your work.15.[100010134]102034

Short Answer

Step by step solution

Block matrix

Multiplication of block matrix

Checking the product

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Geometry

Decision Maths

Logic and Functions

Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Use the given partitions to compute the products in Exercises 15 and 16. Check your work by computing the same products without using a partition. Show all your work.
15. $[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 1 & 3 & 4 \end{matrix}] [\begin{matrix} 1 & 0 \\ 2 & 0 \\ 3 & 4 \end{matrix}]$