Q48E Find matrices such that聽聽det[A... [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 6: Q48E (page 276)

Find matrices such that $d e t [\begin{matrix} A & B \\ C & D \end{matrix}] 鈮� (\det A) (\det D) - (\det B) (\det C)$

Short Answer

Expert verified

Therefore,

$\begin{array}{l} A = D = [\begin{matrix} 1 & 2 \\ 1 & 1 \end{matrix}] \\ B = c = [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}] \end{array}$

Step by step solution

Definition

A determinant is a unique number associated with asquare matrix.

A determinant is a scalar value that is a function of the entries of a square matrix.

It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.

To find the given matrix

For example:

$\begin{array}{l} A = D = [\begin{matrix} 1 & 2 \\ 1 & 1 \end{matrix}] \\ B = c = [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}] \end{array}$

Indeed, we have

$\det A \det D - \det B \det C = (- 1) 路 (- 1) - 0 路 0$

$\det A \det D - \det B \det C = 1$

$\det [\begin{matrix} A & B \\ C & D \end{matrix}] = |\begin{matrix} 1 & 2 & 1 & 1 \\ 1 & 1 & 1 & 1 \\ 1 & 1 & 1 & 2 \\ 1 & 1 & 1 & 1 \end{matrix}|$

role="math" localid="1660629362263" $\det [\begin{matrix} A & B \\ C & D \end{matrix}] = 0$

Therefore,

$\det [\begin{matrix} A & B \\ C & D \end{matrix}] 鈮� (\det A) (\det D) - (\det B) (\det C)$

Therefore,

$\begin{array}{l} A = D = [\begin{matrix} 1 & 2 \\ 1 & 1 \end{matrix}] \\ B = c = [\begin{matrix} 1 & 1 \\ 1 & 1 \end{matrix}] \end{array}$

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91影视

Find matrices such that $d e t [\begin{matrix} A & B \\ C & D \end{matrix}] 鈮� (\det A) (\det D) - (\det B) (\det C)$

Short Answer

Step by step solution

Definition

To find the given matrix

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91影视

Find matrices such thatdet[ABCD]鈮�(detA)(detD)-(detB)(detC)

Short Answer

Step by step solution

Definition

To find the given matrix

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Geometry

Probability and Statistics

Decision Maths

Mechanics Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Find matrices such that $d e t [\begin{matrix} A & B \\ C & D \end{matrix}] 鈮� (\det A) (\det D) - (\det B) (\det C)$