Using determinants, solve the following…

Question 1 Report

Using determinants, solve the following equations simultaneously.

5x — 6y + 4z = 15

7x + 4y — 3z = 19

2x + y + 6z = 46

Answer

Answer Details

System: \(5x-6y+4z=15,\ 7x+4y-3z=19,\ 2x+y+6z=46\). Use Cramer's rule.

\[D=\begin{vmatrix}5&-6&4\\7&4&-3\\2&1&6\end{vmatrix}=5(24+3)+6(42+6)+4(7-8)=135+288-4=419.\] \[D_x=\begin{vmatrix}15&-6&4\\19&4&-3\\46&1&6\end{vmatrix}=15(27)+6(252)+4(-165)=405+1512-660=1257.\] \[D_y=\begin{vmatrix}5&15&4\\7&19&-3\\2&46&6\end{vmatrix}=5(252)-15(48)+4(284)=1260-720+1136=1676.\] \[D_z=\begin{vmatrix}5&-6&15\\7&4&19\\2&1&46\end{vmatrix}=5(165)+6(284)+15(-1)=825+1704-15=2514.\] \[x=\frac{D_x}{D}=\frac{1257}{419}=3,\quad y=\frac{D_y}{D}=\frac{1676}{419}=4,\quad z=\frac{D_z}{D}=\frac{2514}{419}=6.\]

So \(x=3,\ y=4,\ z=6\). Check in equation 2: \(7(3)+4(4)-3(6)=21+16-18=19\).

Read lesson note on Matrices And Linear Transformation (WAEC)

Matrices And Linear Transformation

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Using determinants, solve the following equations simultaneously. 5x — 6y + 4z = 15 7x + 4y — 3z = 19 2x + y + 6z = 46

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