Applications of Matrices and Determinants

Solve the following system of linear equations, using matrix inversion method: 5x+2y=3, 3x+2y=5.
1. x = −1, y = 4
2. x = 4, y = −1
3. x = −4, y = 1
4. None
Solve the system of equations
x₁−x₂=3
2x₁+3x₂+4x₃=17
x₂+2x₃=7
1. 2 , 1 , 4
2. −2 , −1 ,− 4
3. 2 , −1 ,4
4. None
Solve the following system of linear equations,
4x+3y+6z=25,
x+5y+7z=13,
2x+9y+z=1
1. x = -4 , y = -1, z = -2
2. x = 4 , y = -1, z = 2
3. x = -4 , y = 1, z = 2
4. None
Find the condition on a b, and c so that the following system of linear equations has one parameter family of solutions:
x+y+zz=a, x+2y+3z=b, 3x+5y+7z=c
1. a = b + 2c
2. c = a + 2b
3. b = a + 2c
4. None
Solve the following system:
x+2y+3z=0, 3x+4y+4z=0,7x+10y+12z=0
1. x=1, y=2, z=3
2. x=1, y=1, z=1
3. x=0, y=0, z=0
4. None
A square matrix is called a ______matrix if its determinant is not equal to zero.
1. Non-singular
2. singular
3. Inverse
4. None
A square matrix is called a ______matrix if its determinant is equal to zero.
1. Non-singular
2. singular
3. Inverse
4. None
The determinant of a singular matrix is 0 and so a singular matrix has no
1. Non-singular
2. singular
3. Inverse
4. None
A is orthogonal if and only if A is
1. Singular
2. non-singular
3. Inverse
4. None
The process of transformation of an information (plain form) into an unreadable form (coded form).
1. decryption matrix
2. encryption matrix
3. Encryption
4. Decryption
An art of communication between two people by keeping the information not known to others
1. decryption matrix
2. encryption matrix
3. Encryption
4. Cryptography
The matrix used for encryption is
1. decryption matrix
2. encryption matrix
3. Encryption
4. Decryption
The matrix used for decoding is
1. decryption matrix
2. encryption matrix
3. Encryption
4. Decryption
Transformation of the coded message back into original form
1. decryption matrix
2. encryption matrix
3. Encryption
4. Decryption
A system of linear equations having at least one solution is said to be
1. Consistent
2. inconsistent
3. Both a & b
4. None
A system of linear equations having no solution is said to be
1. Consistent
2. inconsistent
3. Both a & b
4. None
An _______ is defined as a matrix which is obtained from an identity matrix by applying only one elementary transformation.
1. Inverse matrix
2. elementary matrix
3. Sub matrix
4. None
Transforming a non-singular matrix A to the form In by applying elementary row operations, is called __________.
1. Gaussian Elimination Method
2. Gauss-Jordan method
3. Matrix Inversion Method
4. None
__________ can be applied only when the coefficient matrix is a square matrix and non-singular.
1. Gaussian Elimination Method
2. Gauss-Jordan method
3. Matrix Inversion Method
4. None
Gaussian Elimination Method can be applied even if the coefficient matrix is singular matrix and rectangular matrix.
1. Gaussian Elimination Method
2. Gauss-Jordan method
3. Matrix Inversion Method
4. None

Applications of Matrices and Determinants

Quiz