Solve Matrix

$$[ \begin{array} { c c c } { 1 } & { 0 } & { 0 } \\ { 2 } & { 1 } & { 0 } \\ { 3 } & { - 2 } & { 1 } \end{array} ) ( \begin{array} { l } { a } \\ { b } \\ { c } \end{array} ) = ( \begin{array} { c } { 10 } \\ { 26 } \\ { 15 } \end{array} )$$

Solve for a, b, c

$$a=10$$

$$b=6$$

$$c=-3$$

Solution Steps

Consider the second equation. Insert the known values of variables into the equation.

$$2\times 10+b=26$$

Multiply 2 and 10 to get 20.

$$20+b=26$$

Subtract 20 from both sides.

$$b=26-20$$

Subtract 20 from 26 to get 6.

$$b=6$$

Consider the third equation. Insert the known values of variables into the equation.

$$3\times 10-2\times 6+c=15$$

Do the multiplications.

$$30-12+c=15$$

Subtract 12 from 30 to get 18.

$$18+c=15$$

Subtract 18 from both sides.

$$c=15-18$$

Subtract 18 from 15 to get -3.

$$c=-3$$

The system is now solved.

$$a=10 b=6 c=-3$$