x1+x2-2x3=b

2x1-x2-3x3=c

under what condition on a,b and c does the system have a solution?( use rref)

John Landry
2022-07-26
Answered

x1+2x2-3x3=a

x1+x2-2x3=b

2x1-x2-3x3=c

under what condition on a,b and c does the system have a solution?( use rref)

x1+x2-2x3=b

2x1-x2-3x3=c

under what condition on a,b and c does the system have a solution?( use rref)

You can still ask an expert for help

Bradley Sherman

Answered 2022-07-27
Author has **17** answers

The system will have a solution irrespective of the values of a,b and c(assuming that a,b and c are constants).

The solution would be

x1 = (-15a + 21b + c)/8

x2 = (a - 3b + c)/8

x3 = (-7a + 5b + c)/8

In case a,b and c are not constants and are dependant on x1 or x2 or x3, then the system will have a solution only when the coefficient matrix (obtained after rearranging the terms so that only constants are on RHS) is invertible. It can be easily checked by just checking the determinant of the coefficient matrix. If the determinant of the matrix turns out to be 0, then the matrix in not invertible and hence the system of equations will not have a solution. however if the determinant of the coefficient matrix is non zero then the inverse of the matrix exists and hence the system of equations will have a solution.

The solution would be

x1 = (-15a + 21b + c)/8

x2 = (a - 3b + c)/8

x3 = (-7a + 5b + c)/8

In case a,b and c are not constants and are dependant on x1 or x2 or x3, then the system will have a solution only when the coefficient matrix (obtained after rearranging the terms so that only constants are on RHS) is invertible. It can be easily checked by just checking the determinant of the coefficient matrix. If the determinant of the matrix turns out to be 0, then the matrix in not invertible and hence the system of equations will not have a solution. however if the determinant of the coefficient matrix is non zero then the inverse of the matrix exists and hence the system of equations will have a solution.

asked 2022-09-13

Find all natural values of x for which the inequality is true: 3 1\8<25\x<8 1\3

asked 2022-07-26

Name three numbers between 0.33 and 0.34.

asked 2021-06-08

In January, the average high temperature for Calgary is

asked 2022-03-29

asked 2022-08-08

Solve the equation:

$3(x-9)=6(x+4)-x$

$3(x-9)=6(x+4)-x$

asked 2022-07-25

Write the expression as the sine, cosine, or tangent of adouble angle. Then find the exact value of the expression.

${\mathrm{cos}}^{2}15-{\mathrm{sin}}^{2}15$

${\mathrm{cos}}^{2}15-{\mathrm{sin}}^{2}15$

asked 2022-05-12

How do you solve and graph $5\ge 7+y$ ?