Cramer’s rule of matrix
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Cramer's rule is a method for solving systems of linear equations. It uses determinants to find the solutions for the variables. For two equations with two unknowns, the solutions are found as the ratio of two determinants. For three equations with three unknowns, Cramer's rule can also be applied by writing the solutions as ratios of determinants. Some examples are provided to demonstrate solving systems of two and three equations using Cramer's rule.
Cramer’s rule of matrix
- 2. Cramer’s rule is a method for solving linear simultaneous equations. It makes use to determinats and so the knowledge of these necessary before proceeding. INTRODUCTION
- 3. Cramer’s Rule - two equations If we are given a pair of simultaneous equations a1x + b1y = d1 a2x + b2y = d2 then x, and y can be found from Example Solve the equations 3x + 4y = −14 −2x − 3y = 11 Solution Using Cramer’s rule we can write the solution as the ratio of two determinants.
- 4. The solution of the simultaneous equations is then x = 2, y = −5. The solution set is {(2,-5)}
- 5. Cramer’s rule - three equations For the case of three equations in three unknowns: If a1x + b1y + c1z = d1 a2x + b2y + c2z = d2 a3x + b3y + c3z = d3
- 6. Exercises Use Cramer’s rule to solve the following sets of simultaneous equations. a) 7x + 3y = 15 −2x + 5y = -16 b) -x + 2y + 3z = -7 -4x - 5y + 6z = -13 7x - 8y - 9z = 39