WorksheetsLinear Algebra Quiz
Total questions: 14
Worksheet time: 7mins
Which of the following is NOT an elementary row operation on a matrix?
Interchanging any two rows
Multiplying all elements of a row by a nonzero constant
Adding to one row a constant multiple of another row
Adding all rows together into a single row
The rank of the matrix 123246105 is:
1
2
3
0
If the rank of the coefficient matrix A and the augmented matrix [A∣B] are equal and equal to the number of unknowns, then the system has:
No solution
Infinite solutions
Unique solution
Undetermined solution
What is the main purpose of the Gauss elimination method?
To find the determinant of a matrix
To solve a system of linear equations
To calculate the inverse of a matrix
To find the eigenvalues of a matrix
The Gauss-Seidel method is classified as a:
Direct method
Iterative method
Exact method
Deterministic method
Which of the following is true for eigenvectors corresponding to distinct eigenvalues?
They are orthogonal
They are linearly dependent
They are linearly independent
They are zero vectors
The Rayleigh power method is mainly used to find:
All eigenvalues of a matrix
The largest eigenvalue and corresponding eigenvector
The smallest eigenvalue
Inverse of the matrix
The matrix P used in diagonalization P-1AP=D consists of:
Eigenvalues of A
Eigenvectors of A as columns
Rows of A
Diagonal elements of A
A set of vectors is linearly independent if:
At least one vector can be written as a linear combination of others
The only solution to a1v1+⋯+anvn=0 is all ai=0
The vectors are orthogonal
The vectors span the vector space
The number of vectors in any basis of a finite-dimensional vector space is called:
Its order
Its dimension
Its determinant
Its rank
If T:R2→R2 is given by T(x,y)=(x,0), then T(1,1) is:
(1,1)
(1,0)
(0,1)
(0,0)
The rank of a linear transformation is:
The number of linearly independent vectors in its domain
The maximum number of linearly independent vectors in its codomain
The trace of the transformation matrix
The number of basis vectors in the domain
Which of the following is always true for any linear transformation T:Rn→Rm?
nullity(T)=m-n
rank(T)+nullity(T)=n
rank(T)+nullity(T)=m
nullity(T)=n+m
The dimension of the kernel of a linear transformation is called:
Rank
Nullity
Span
Basis size
