30 Questions
What is the condition for two matrices A and B to be equal?
They have the same order and corresponding elements are equal
What is the order of the matrix [5 0 3]?
1×3
What is the characteristic of a singleton matrix?
It has only one element
What is the order of the column matrix [[2][3][−6]]?
3×1
What is the notation used to represent the element at the ith row and jth column of a matrix A?
a_{ij}
What is the arrangement of numbers enclosed by in a matrix?
Small or big brackets
What is the notation used to represent a matrix?
Capital letters
What is the condition for a square matrix to be a diagonal matrix?
All elements of the principal diagonal are non-zero.
What is the number of zeros in a diagonal matrix of order n × n?
n^2 - n
What is the notation for a diagonal matrix of order n × n with diagonal elements d1, d2,..., dn?
diag[d1, d2,..., dn]
What is the characteristic of an identity matrix?
All elements in the main diagonal are one and rest are zero.
What is a solution of a system of equations?
A value of x and y that simultaneously satisfy all the equations
What is a consistent system of equations?
A system with one or more solutions
What is the rank of the matrix if x + c ≠ 0?
3
What is the matrix representation of the system of linear equations?
AX = B
What is a homogeneous system of linear equations?
A system with a zero constant term
How many methods are there to solve a non-homogeneous system of linear equations?
Three methods
What is an example of a consistent system of linear equations?
2x + 3y = 5, 4x + 6y = 10
What is the matrix A in the system of linear equations AX = B?
The coefficient matrix of the system of linear equations
What is the echelon form of the matrix?
A matrix with leading entries in each row
When is a system of linear equations guaranteed to have an infinite number of solutions?
When the number of equations is less than the number of unknowns and the system is consistent
What is the purpose of reducing the augmented matrix to Echelon form in the rank method?
To solve for the unknowns in a system of linear equations
What is the relationship between the rank of A and the rank of [A : B] in a system of linear equations AX = B?
The rank of A is equal to the rank of [A : B] if the system is consistent
What is the condition for a system of linear equations to have a unique solution?
The determinant of the coefficient matrix must be non-zero
What is the purpose of finding the number of non-zero rows in A and [A : B] in the rank method?
To determine the rank of the matrix
What is the purpose of reducing the augmented matrix to Echelon form in the rank method?
To find the solution of the system of linear equations
What is the condition for a system of linear equations to have a unique solution?
The number of equations is equal to the number of unknowns
What is the rank of the matrix A if the system of linear equations AX = B has a unique solution?
The number of non-zero rows of A
What is the condition for a system of linear equations to have an infinite number of solutions?
The number of equations is less than the number of unknowns
What is the determinant of the matrix A if the system of linear equations AX = B has no solution?
Zero
Learn about the conditions for two matrices to be equal and different types of matrices, including row matrices and row vectors. Understand the concept of order and elements of matrices.
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