Q 63E In Exercises 55 through 64, find... [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: Q 63E (page 86)

In Exercises 55 through 64, find all matricesX that satisfy the given matrix equation. 63.
$[\begin{matrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{matrix}] X = I_{3}$

Short Answer

Expert verified

There is no such matrix X exists such that $[\begin{matrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{matrix}] X = I_{3}$ .

Step by step solution

Assuming the matrix

Since, the product of matrix $3 脳 2$ and matrix X gives the matrix of order $3 脳 3$ then the order of matrix X should be $2 脳 3$ .

Let the matrix be $X = [\begin{matrix} a & c & e \\ b & d & f \end{matrix}]$

We know the matrix $I_{3} = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$ .

Then the equation will become:

$[\begin{matrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{matrix}] [\begin{matrix} a & c & e \\ b & d & f \end{matrix}] = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$

Solving the Matrix

To solve the given matrix equation, first simplify the left-hand side matrix.

$[\begin{matrix} a + 4 b & c + 4 d & e + 4 f \\ 2 a + 5 b & 2 c + 5 d & 2 e + 5 f \\ 3 a + 6 b & 3 c + 6 d & 3 e + 6 f \end{matrix}] = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]$

Now equating the left-hand and right-hand matrix.

$a + 4 b = 1 c + 4 d = 0 e + 4 f = 0 2 a + 5 b = 0 2 c + 5 d = 1 2 e + 5 f = 0 3 a + 6 d = 0 3 c + 6 d = 0 3 e + 6 f = 1$

On solving the above equations, we will get $0 = 1$ , which is not possible for any value.

Hence, there is no such matrix X that exists such that

[\begin{matrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{matrix}] X = I_{3}

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91影视

In Exercises 55 through 64, find all matricesX that satisfy the given matrix equation. 63.
$[\begin{matrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{matrix}] X = I_{3}$

Short Answer

Step by step solution

Assuming the matrix

Solving the Matrix

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91影视

In Exercises 55 through 64, find all matricesX that satisfy the given matrix equation. 63.142536X=I3

Short Answer

Step by step solution

Assuming the matrix

Solving the Matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Logic and Functions

Applied Mathematics

Geometry

Pure Maths

Study anywhere. Anytime. Across all devices.

In Exercises 55 through 64, find all matricesX that satisfy the given matrix equation. 63.
$[\begin{matrix} 1 & 4 \\ 2 & 5 \\ 3 & 6 \end{matrix}] X = I_{3}$