`\color{green} ✍️` Let us express the system of linear equations as matrix equations and solve them using inverse of the coefficient matrix.
Consider the system of equations
`a_1 x + b_1 y + c_1 z = d_1`
`a_2 x + b_2 y + c_2 z = d_2`
`a_3 x + b_3 y + c_3 z = d_3`
Let `A = [ (a_1, b_1, c_1), ( a_2, b_2, c_2 ), (a_3, b_3, c_3) ] , X = [ (x), (y), (z) ]` and `B = [ (d_1), ( d_2),(d_3) ]`
Then, the system of equations can be written as, `AX = B,` i.e.,
`color{orange}{[ (a_1, b_1, c_1 ), ( a_2, b_2 , c_2 ), ( a_3, b_3 , c_3) ] [ (x), (y), (z) ] = [ (d_1), (d_2), (d_3) ]}`
`\color{green} ✍️` Let us express the system of linear equations as matrix equations and solve them using inverse of the coefficient matrix.
Consider the system of equations
`a_1 x + b_1 y + c_1 z = d_1`
`a_2 x + b_2 y + c_2 z = d_2`
`a_3 x + b_3 y + c_3 z = d_3`
Let `A = [ (a_1, b_1, c_1), ( a_2, b_2, c_2 ), (a_3, b_3, c_3) ] , X = [ (x), (y), (z) ]` and `B = [ (d_1), ( d_2),(d_3) ]`
Then, the system of equations can be written as, `AX = B,` i.e.,
`color{orange}{[ (a_1, b_1, c_1 ), ( a_2, b_2 , c_2 ), ( a_3, b_3 , c_3) ] [ (x), (y), (z) ] = [ (d_1), (d_2), (d_3) ]}`