Q1.3 33E Let A be the n脳n聽聽聽matrix wi... [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 1: Q1.3 33E (page 36)

Let A be the $n 脳 n$ matrix with all 1鈥檚 on the diagonal and all 0鈥檚 above and below the diagonal. What is $A \overset{鈫�}{x}$ , where $\overset{鈫�}{x}$ is a vector in $R^{n}$ ?

Short Answer

Expert verified

$A \overset{鈫�}{x}$ for a matrix A with all 1鈥檚 on the diagonal and all 0鈥檚 above and below the diagonal is, $A \overset{鈫�}{x}$ is, $[x y z]$ .

Step by step solution

Consider the matrix

IfA is an n x m matrix with row vectors $\overset{鈫�}{蝇_{1}}, . . . \overset{鈫�}{蝇_{n}}$ and $\overset{鈫�}{x}$ is a vector in $R^{m}$ then,

$A \overset{鈫�}{x} = [\begin{matrix} - {\overset{鈫�}{蝇}}_{1} - \\ 鈰� \\ - \overset{鈫�}{蝇_{n}} - \end{matrix}] \overset{鈫�}{x} [\begin{matrix} - {\overset{鈫�}{蝇}}_{1} . \overset{鈫�}{x} - \\ 鈰� \\ - \overset{鈫�}{蝇_{n}} . \overset{鈫�}{x} - \end{matrix}]$

Let the vector is,

$\overset{鈫�}{x} = [\begin{matrix} x \\ y \\ z \end{matrix}]$

The matrix A with all 1鈥檚 on the diagonal and all 0鈥檚 above and below the diagonal is,

$[\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$

Perform the multiplication operation

The system $A \overset{鈫�}{x}$ is,

role="math" localid="1664201537736" $A \overset{鈫�}{x} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} x \\ y \\ z \end{matrix}] A \overset{鈫�}{x} = [\begin{matrix} x \\ y \\ z \end{matrix}]$

Hence, $[\begin{matrix} x \\ y \\ z \end{matrix}]$ is the value of $A \overset{鈫�}{x}$ for the matrix A with all 1鈥檚 on the diagonal and all 0鈥檚 above and below the diagonal.

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91影视

Let A be the $n 脳 n$ matrix with all 1鈥檚 on the diagonal and all 0鈥檚 above and below the diagonal. What is $A \overset{鈫�}{x}$ , where $\overset{鈫�}{x}$ is a vector in $R^{n}$ ?

Short Answer

Step by step solution

Consider the matrix

Perform the multiplication operation

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91影视

Let A be the n脳nmatrix with all 1鈥檚 on the diagonal and all 0鈥檚 above and below the diagonal. What is Ax鈫� , where x鈫� is a vector in Rn?

Short Answer

Step by step solution

Consider the matrix

Perform the multiplication operation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Decision Maths

Discrete Mathematics

Probability and Statistics

Statistics

Study anywhere. Anytime. Across all devices.

Let A be the $n 脳 n$ matrix with all 1鈥檚 on the diagonal and all 0鈥檚 above and below the diagonal. What is $A \overset{鈫�}{x}$ , where $\overset{鈫�}{x}$ is a vector in $R^{n}$ ?