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popularize the technique.

Overwork combined with a fall from a carriage led to his death at the age of 48. Cramer was apparently a good-natured
and pleasant person with broad interests. He wrote on philosophy of law and government and the history of mathematics.
He served in public office, participated in artillery and fortifications activities for the government, instructed workers on
techniques of cathedral repair, and undertook excavations of cathedral archives. Cramer received numerous honors for his
activities.

Remark To solve a system of equations in unknowns by Cramer's rule, it is necessary to evaluate determinants of

matrices. For systems with more than three equations, Gaussian elimination is far more efficient. However, Cramer's rule
does give a formula for the solution if the determinant of the coefficient matrix is nonzero.

Exercise Set 2.1

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Let
1.

(a) Find all the minors of .

(b) Find all the cofactors.

Let
2.

Find and
(a)

(b) and

(c) and

(d) and