Show that the determinant of the matrix is equal to the determinant of its transpose by expanding along the third row ofA and the third column of AA= 1 0-2-2-3Write an expression for A| by expanding along the third row of A.-488-088-088(Type the terms of your expression in the same order as they appear in the original expression.)55 -1 0View an example+|A|=|F6Q Search&F709LEGIONF8(F9)F10OIClear allF11+F12Insert4Check answerDelete

Answered: Show that the determinant of the matrix…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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Show that the determinant of the matrix is equal to the determinant of its transpose by expanding along the third row of
A and the third column of A
A= 1 0
-
2-2-3
Write an expression for A| by expanding along the third row of A.
-488-088-088
(Type the terms of your expression in the same order as they appear in the original expression.)
5
5 -1 0
View an example
+
|A|=|
F6
Q Search
&
F7
09
LEGION
F8
(
F9
)
F10
OI
Clear all
F11
+
F12
Insert
4
Check answer
Delete

Expert Solution

Step 1: Solution

Given matrix:

$A equals open square brackets table row 2 cell negative 2 end cell cell negative 3 end cell row 1 0 5 row 5 cell negative 1 end cell 0 end table close square brackets$

We have to show that the determinant of the matrix is equal to the determinant of its transpose by expanding along the third row of $A$ and the third column of $A to the power of T$

Notation: $D e t left parenthesis A right parenthesis equals open vertical bar A close vertical bar$