A system of two linear equations can be written as the single matrix equation and solved b...

A system of two linear equations

can be written as the single matrix equation

and solved by the method of Exercise 1, provided the coefficient matrix is not singular. Larger systems can be solved by the same means. Solve each of the following systems using this approach.

(a)

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(b)

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(c)

Exercise 1

Given an n × n invertible matrix A and n × 1 column matrix b, we can solve the equation Ax = b for the unknown vector x by multiplying both sides by A−1 and using various properties of matrix arithmetic to obtain x = A−1b. Find all 2 × 1 or 3 × 1 matrix solutions x to the following equations, where it is possible.

(a)

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(b)

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(c)

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(d)

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(e)

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(f)