Solve the matrix equation: 4[2x,y,3z]+3[2,−4,6]=[20,−4,54]

Question
Systems of equations
asked 2021-01-02
Solve the matrix equation: \(\displaystyle{4}{\left[{2}{x},{y},{3}{z}\right]}+{3}{\left[{2},−{4},{6}\right]}={\left[{20},−{4},{54}\right]}\)

Answers (1)

2021-01-03
Solving this system means solving each of the following equations: \(\displaystyle{8}{x}+{6}={20},\)
\(\displaystyle{4}{y}−{12}=−{4},\)
and
\(\displaystyle{12}{z}+{18}={54}\)
You can obtain these equations by performing scalar multiplication on the vectors given. From here, you just use basic algebra to find that the solutions are as follows:
\(\displaystyle{x}={\frac{{{14}{\left\lbrace{8}\right\rbrace},{y}={2},{\quad\text{and}\quad}{z}={3}.}}{}}\)
0

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