Chapter 3: Q8MP (page 185)

Given
$A = (\begin{matrix} 1 & 0 & 2 i \\ i & - 3 & 0 \\ 1 & 0 & i \end{matrix})$ Find $A^{T}, A, A^{⧾}, A^{- 1}$

Short Answer

Expert verified

$= \frac{1}{3 i} (\begin{matrix} - 3 i & 0 & 6 i \\ 1 & - i & - 2 \\ 3 & 0 & - 3 \end{matrix})$

Step by step solution

Step 1: Given information

The matrix is given as $A = (\begin{matrix} 1 & 0 & 2 i \\ i & - 3 & 0 \\ 1 & 0 & i \end{matrix})$

Definition of Matrix

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object.

Verify the given statement

As the given matrix is:

$A = (\begin{matrix} 1 & 0 & 2 i \\ i & - 3 & 0 \\ 1 & 0 & i \end{matrix})$

Hence,

Since $A$ is the conjugate matrix of A

Then,

$A = (\begin{matrix} 1 & 0 & - 2 i \\ - i & - 3 & 0 \\ 1 & 0 & - i \end{matrix})$

Since $A^{I}$ is the transpose $A$

Hence,

$A^{A} = (\begin{matrix} 1 & - i & 1 \\ 0 & - 3 & 0 \\ - 2 i & 0 & - i \end{matrix})$

Now evaluating the inverse of matrix A

Since,

det A=3i +2i(3)

Now,

$A d j A = (\begin{matrix} 3 i & 0 & 6 i \\ 1 & - i & - 2 \\ 3 & 0 & 3 \end{matrix})$

Then,

role="math" localid="1659078880287" $A^{- 1} = \frac{A d j i}{|A|} = \frac{1}{3 i} (\begin{matrix} - 3 i & 0 & 6 i \\ 1 & - i & - 2 \\ 3 & 0 & - 3 \end{matrix})$

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Given
$A = (\begin{matrix} 1 & 0 & 2 i \\ i & - 3 & 0 \\ 1 & 0 & i \end{matrix})$ Find $A^{T}, A, A^{⧾}, A^{- 1}$

Short Answer

Step by step solution

Step 1: Given information

Definition of Matrix

Verify the given statement

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Most popular questions from this chapter

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GivenA=(102ii-3010i)FindAT,A,A⧾,A-1

Short Answer

Step by step solution

Step 1: Given information

Definition of Matrix

Verify the given statement

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Thermodynamics

Fundamentals of Physics

Translational Dynamics

Mechanics and Materials

Electricity and Magnetism

Medical Physics

Study anywhere. Anytime. Across all devices.

Given
$A = (\begin{matrix} 1 & 0 & 2 i \\ i & - 3 & 0 \\ 1 & 0 & i \end{matrix})$ Find $A^{T}, A, A^{⧾}, A^{- 1}$