Difference between cramer's rule and Matrix method and when to use which one - Maths - Determinants

Question

Difference between cramer's rule and Matrix method and when to
use which one

Harleen Birdi · Accepted Answer

Dear Student!!

You can view the solving of system of simultaneous linear equations by matrix method at the study material given in the meritnation site (Chapter: 4 Determinants, Lesson: 7).

Also, one can solve the system of simultaneous linear equations by the method of Cramer's rule.

The rule is given below.

For the system (two variables) $a_{1} x + b_{1} y = c_{1}, a_{2} x + b_{2} y = c_{2}$ , solution is given by

$x = \frac{D_{1}}{D_{2}}, y = \frac{D_{2}}{D}, where D = | \begin{matrix} a_{1} & b_{1} \\ a_{2} & b_{2} \end{matrix} |, D_{1} = | \begin{matrix} c_{1} & b_{1} \\ c_{2} & b_{2} \end{matrix} | and D_{2} = | \begin{matrix} a_{1} & c_{1} \\ a_{2} & c_{2} \end{matrix} |$ provided that D ≠ 0.

For the system (three variables) $a_{1} x + b_{1} y + c_{1} z = d_{1}, a_{2} x + b_{2} y + c_{2} z = d_{2}, a_{3} x + b_{3} y + c_{3} z = d_{3}$ , solution is given by

$x = \frac{D_{1}}{D_{2}}, y = \frac{D_{2}}{D}, z = \frac{D_{3}}{D}, where D = | \begin{matrix} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{matrix} |, D_{1} = | \begin{matrix} d_{1} & b_{1} & c_{1} \\ d_{2} & b_{2} & c_{2} \\ d_{3} & b_{3} & c_{3} \end{matrix} |, D_{2} = | \begin{matrix} a_{1} & d_{1} & c_{1} \\ a_{2} & d_{2} & c_{2} \\ a_{3} & d_{3} & c_{3} \end{matrix} | and D_{3} = | \begin{matrix} a_{1} & b_{1} & d_{1} \\ a_{2} & b_{2} & d_{2} \\ a_{3} & b_{3} & d_{3} \end{matrix} |$ provided that D ≠ 0.

Cramer's rule is a direct formula.

You can solve questions by any one of the methods.

(But it is advisable for you to solve problems by matrix method as cramer's rule is not under CBSE syllabus).

Best wishes..!!

Difference between cramer's rule and Matrix method.....and when to use which one.....