Use Cramer’s rule to compute the solutions of the systems in Exercises 1−6.
5.
To compute: The solutions of the systems using Cramer’s rule.
Answer to Problem 5E
The solutions of the systems using Cramer’s rule is
Explanation of Solution
Given:
The equations are,
Rule used:
Cramer’s Rule:
Let A be an invertible
Calculation:
The given system is of the form
Check the matrix
Here, determinant of the matrix is non-zero, the matrix is invertible.
The matrix
Thus, the matrix
That is,
From Cramer rule, the unique solution x of
Obtain the determinant of the matrix
Obtain the determinant of the matrix
Obtain the determinant of the matrix
Thus,
The first entry of the solution obtained by substituting 1 for i in the equation
Similarly, the second entry of the solution obtained by substituting 2 for i in the equation
Similarly, the third entry of the solution obtained by substituting 3 for i in the equation
Hence, the solutions of the systems using Cramer’s rule is
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