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In this lesson, we will learn how to express a system of linear equations in matrix form and how to solve this system by the matrix inversion method.

Q1:

Solve the system of the linear equations − 𝑥 + 𝑦 + 𝑧 = 8 , − 2 𝑥 + 𝑦 − 𝑧 = − 5 , and 6 𝑥 − 3 𝑦 = − 6 using the inverse of a matrix.

Q2:

Use the inverse of a matrix to solve the system of linear equations − 4 𝑥 − 2 𝑦 − 9 𝑧 = − 8 , − 3 𝑥 − 2 𝑦 − 6 𝑧 = − 3 , and − 𝑥 + 𝑦 − 6 𝑧 = 7 .

Q3:

Solve the system of the linear equations 3 𝑥 + 2 𝑦 = 8 and 6 𝑥 − 9 𝑦 = 3 using the inverse of a matrix.

Q4:

Consider the simultaneous equations

Express the simultaneous equations as a single matrix equation.

Write down the inverse of the coefficient matrix.

Multiply through by the inverse, on the left-hand side, to solve the matrix equation.

Q5:

Using matrix inverses, solve the following for .

Q6:

Use matrices to solve the system

Q7:

Use matrices to solve the following system of equations.

Q8:

Solve this system of equations using the inverse matrix.

Give your solution as an appropriate matrix whose elements are expressed in terms of , , , and .

Q9:

Q10:

Consider the system of equations

Express the system as a single matrix equation.

Work out the inverse of the coefficient matrix.

Q11:

Q12:

Given find the matrix 𝐴 .

Q13:

Given that the solution set of the equation 𝑎 𝑥 + 𝑏 𝑥 + 7 = 0 2 is { − 1 , − 7 } , use matrices to find the constants 𝑎 and 𝑏 .

Q14:

Solve the following for .

Q15:

Q16: