In this lesson, we will learn how to solve a system of three linear equations using the inverse of the matrix of coefficients.
Students will be able to
Q1:
Consider the system of equations 2π+2π+4π=4βπβπβπ=142π+5π+6π=10.
Express the system as a single matrix equation.
Work out the inverse of the coefficient matrix.
Multiply through by the inverse, on the left-hand side, to solve the matrix equation.
Q2:
Use matrices to solve the following system of equations: βπ₯+8π¦β3π§=β10,4π₯β3π¦+8π§=12,6π₯β12π¦+19π§=18.
Q3:
Use the inverse of a matrix to solve the system of linear equations β4π₯β2π¦β9π§=β8, β3π₯β2π¦β6π§=β3, and βπ₯+π¦β6π§=7.
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