Use Cramer's rule to solve the system of equations, if D=0, use another method to determine the solution set. 5x+5y−10z=8 2x+y−z=7 −x−y+2z=3 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution set is (_,_,_). (Type integers or simplified fractions.) B. There are infinitely many solutions. The solution set is (_,_,z), where z is any real number. (Simplify your answers. Use integers or fractions for any numbers in the expressions.) C. There is no solution. The solution set is ⊘.

Question

Use Cramer&#039;s rule to solve the system of equations, if D=0, use another method to determine the solution set. 5x+5y−10z=8 2x+y−z=7 −x−y+2z=3 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution set is (_,_,_). (Type integers or simplified fractions.) B. There are infinitely many solutions. The solution set is ​​​​​​​(_,_,z), where z is any real number. (Simplify your answers. Use integers or fractions for any numbers in the expressions.) C. There is no solution. The solution set is ⊘.

cheekabooy · Accepted Answer

Step 1 Use cramer’s rule to solve the system of equation. If D = 0, use another method to determine the solution set 5x+5y−10z=8 2x+y−z=7 −x−y+2z=3 Step 2 First, find the determinant of the coefficient matrix. A=[55−1021−1−1−12] and b=[873] D=|A| ⇒D=5(2−1)−5(4−1)−10(−2+1) ⇒D=5−15+10 ⇒D=0 Step 3 To solve the system of equation with Gaussian elimination using augmented matrix Write as an augmented matrix [A:b]=[55−10821−17−1−123] Apply row operation R3→R3+15R1R2→R2−25R1→ [55−1080−13195000235] Rank (A)=2 and Rank (A:b)=3 ⇒(A)≠Rank(A:b) ⇒ System of equation has no solution Step 4 Answer: (C ) There is no solution. The solution set is empty

Use Cramer's rule to solve the system of equations, if D=0, use another me

Answered question

Answer & Explanation

New Questions in Pre-Algebra