Chapter 4 Determinants Ex 4.6 Solutions
Question - 1 : - Examine the consistency of the system ofequations.
x + 2y = 2
2x + 3y = 3
Answer - 1 : -
The given system of equations is:
x + 2y = 2
2x + 3y = 3
The given system of equations can be written inthe form of AX = B, where
∴ A is non-singular.
Therefore, A−1 exists.
Hence, the given system of equations isconsistent.
Question - 2 : - Examine the consistency of the system ofequations.
2x − y = 5
x + y = 4
Answer - 2 : -
The given system of equations is:
2x − y = 5
x + y = 4
The given system of equations can be written inthe form of AX = B, where
∴ A is non-singular.
Therefore, A−1 exists.
Hence, the given system of equations isconsistent.
Question - 3 : - Examine the consistency of the system ofequations.
x + 3y = 5
2x + 6y = 8
Answer - 3 : -
The given system of equations is:
x + 3y = 5
2x + 6y = 8
The given system of equations can be written inthe form of AX = B, where
∴ A is asingular matrix.
Thus, the solution of the given system ofequations does not exist. Hence, the system of equations is inconsistent.
Question - 4 : - Examine the consistency of the system ofequations.
x + y + z = 1
2x + 3y + 2z =2
ax + ay +2az = 4
Answer - 4 : -
The given system of equations is:
x + y + z = 1
2x + 3y + 2z =2
ax + ay + 2az = 4
This system of equations can be written in theform AX = B, where
∴ A is non-singular.
Therefore, A−1 exists.
Hence, the given system of equations isconsistent.
Question - 5 : - Examine the consistency of the system ofequations.
3x − y − 2z = 2
2y − z = −1
3x − 5y = 3
Answer - 5 : -
The given system of equations is:
3x − y − 2z = 2
2y − z = −1
3x − 5y = 3
This system of equations can be written in theform of AX = B, where
∴ A is a singular matrix.
Thus, the solution of the given system ofequations does not exist. Hence, the system of equations is inconsistent.
Question - 6 : - Examine the consistency of the system ofequations.
5x − y + 4z =5
2x + 3y + 5z =2
5x − 2y +6z = −1
Answer - 6 : -
The given system of equations is:
5x − y + 4z =5
2x + 3y + 5z =2
5x − 2y + 6z =−1
This system of equations can be written in theform of AX = B, where
∴ A is non-singular.
Therefore, A−1 exists.
Hence, the given system of equations isconsistent.
Question - 7 : - Solve system of linear equations, using matrixmethod.
Answer - 7 : -
The given system of equations can be written inthe form of AX = B, where
Thus, A is non-singular.Therefore, its inverse exists.
Question - 8 : - Solve system of linear equations, using matrixmethod.
Answer - 8 : -
The given system of equations can be written inthe form of AX = B, where
Thus, A is non-singular.Therefore, its inverse exists.
Question - 9 : - Solve system of linear equations, using matrixmethod.
Answer - 9 : -
The given system of equations can be written inthe form of AX = B, where
Thus, A is non-singular.Therefore, its inverse exists.
Question - 10 : - Solve system of linear equations, using matrix method.
5x + 2y = 3
3x + 2y = 5
Answer - 10 : -
The given system of equations can be written inthe form of AX = B, where
Thus, A is non-singular.Therefore, its inverse exists.