Q 64E 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 64E (page 86)

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

Short Answer

Expert verified

The matrix that will satisfy the equation will be $[\begin{matrix} \frac{- 5}{3} + e & \frac{4}{3} - 2 e \\ \frac{2}{3} + f & \frac{- 1}{3} - 2 f \\ e & f \end{matrix}]$ , where e,f are constants.

Step by step solution

Assuming the matrix

Since, the product of matrix $2 脳 3$ and matrix X gives the matrix of orderrole="math" localid="1664196259800" $2 脳 2$ then the order of matrix should be $3 脳 2$ .

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

Then the equation will become

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

Solving the Matrix

For solving the given matrix equation first of multiply the left-hand side matrix.

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

Now equating the left hand and right-hand matrix.

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

On solving the above equations, we will get

$a = \frac{- 5}{3} + e, b = \frac{4}{3} - 2 e, c = \frac{2}{3} + f, d = \frac{- 1}{3} - 2 f, e = e, f = f$

Hence, the matrix X which satisfied the given equation is $[\begin{matrix} \frac{- 5}{3} + e & \frac{4}{3} - 2 e \\ \frac{2}{3} + f & \frac{- 1}{3} - 2 f \\ e & f \end{matrix}]$ , where are constants.

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91影视

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

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. 64.123456X=I2

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

Probability and Statistics

Geometry

Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

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