Question

3x+4y+5z=18. 2x-y+8z=4. 5x-2y+7z=20
solve the equation by matrix form
.​

Answer 1

Finding Determinant

D = $\left[\begin{array}{ccc}3&4&5\\2&-1&8\\5&-2&7\end{array}\right]$

=3(-7+16)-4(14-40)+5(-4+5) = 136

Dx = $\left[\begin{array}{ccc}18&4&5\\13&-1&8\\20&-2&7\end{array}\right]$

=18(-7+16)-4(91-160)+5(-26+20) = 408

Dy = $\left[\begin{array}{ccc}3&18&5\\2&13&8\\5&20&7\end{array}\right]$

=3(91-160)-18(14-40)+5(40-65) = 136

Dz = $\left[\begin{array}{ccc}3&4&18\\2&-1&13\\5&-2&20\end{array}\right]$

=3(-20+26)-4(40-65)+18(-4+5) = 136

Therefore x = Dx/D  = 408/136 = 3

y = Dy/D = 136/136 = 1

z= Dz/D = 136/136 = 1