5.C) calculate the determinant 5c.H = (1 2 3 1 1 1 2 4 6 ) ;J = (2 4 2 1 6 1 2 9 2 ) ;K = (1 2 3 0 1 1 2 5 0 )Hitunglah determinannya

Answered: H = (123 11 1 2 4 6 ) ; J = (2 4 2 1 6…

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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5.C) calculate the determinant

5c.
H = (1 2 3 1 1 1 2 4 6 ) ;
J = (2 4 2 1 6 1 2 9 2 ) ;
K = (1 2 3 0 1 1 2 5 0 )
Hitunglah determinannya

Expert Solution

Step 1

The objective is to find the determinant for $H = (1 2 3 1 1 1 2 4 6)$ , $J = (2 4 2 1 6 1 2 9 2)$ and $K = (1 2 3 0 1 1 2 5 0)$ .

The determinant of $H = (1 2 3 1 1 1 2 4 6)$ is,

$\begin{array}{rcl} H & = & |[\begin{matrix} 1 & 2 & 3 \\ 1 & 1 & 1 \\ 2 & 4 & 6 \end{matrix}]| \\ = & 1 (6 - 4) - 2 (6 - 2) + 3 (4 - 2) \\ = & 2 - 4 + 6 \\ = & 4 \end{array}$

The determinant for $J = (2 4 2 1 6 1 2 9 2)$ is,

$\begin{array}{rcl} J & = & |\begin{matrix} 2 & 4 & 2 \\ 1 & 6 & 1 \\ 2 & 9 & 2 \end{matrix}| \\ = & 2 (12 - 9) - 4 (2 - 2) + 2 (9 - 12) \\ = & 6 - 6 \\ = & 0 \end{array}$

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