Let A*X = B, be a system of

Richard Smith

Richard Smith

Answered question

2022-07-31

Let A*X = B, be a system of linear equations where A is a 3×3 matrix. Suppose det A = 8, det Ax = 24, det Ay = 16 and det Az = 0 then the solution set using Cramer’s rule is given by:

Answer & Explanation

Jazz Frenia

Jazz Frenia

Skilled2023-05-29Added 106 answers

To solve the system of linear equations using Cramer's rule, we need to find the values of the variables x, y, and z. Given that:
- det(A)=8
- det(Ax)=24
- det(Ay)=16
- det(Az)=0
We can use Cramer's rule to find the values of x, y, and z by dividing the determinants of the matrices involving the variables by the determinant of A.
Cramer's rule states that if we have a system of linear equations represented by the matrix equation A * X = B, then the solution set is given by:
X=[det(Ax)det(A)det(Ay)det(A)det(Az)det(A)]
Substituting the given values, we have:
X=[24816808]=[320]
Therefore, the solution set using Cramer's rule is:
x=3
y=2
z=0

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