Question 1 |
Let M be a real 
matrix. Consider the following statements:
S1:
has 4 linearly independent eigenvectors.
S2:
has 4 distinct eigenvalues.
S3:
is non-singular (invertible).
Which one among the following is TRUE?
matrix. Consider the following statements: S1:
has 4 linearly independent eigenvectors. S2:
has 4 distinct eigenvalues. S3:
is non-singular (invertible). Which one among the following is TRUE?
S1 implies S2 | |
S1 implies S3 | |
S2 implies S1 | |
S3 implies S2 |
Question 1 Explanation:
The Correct Answer Among All the Options is C
Eigen vectors corresponding to distinct eigen values are linearly independent.
So, “S2 implies S1”.
->We know that if a matrix A has'n' distinct eigen values then A has 'n' linearly independenteigenvectors
.Therefore"S2 implies S1"
Eigen vectors corresponding to distinct eigen values are linearly independent.
So, “S2 implies S1”.
->We know that if a matrix A has'n' distinct eigen values then A has 'n' linearly independenteigenvectors
.Therefore"S2 implies S1"
Question 2 |
The value of p such that the vector 
is an eigenvector of the matrix 
is ________.
is an eigenvector of the matrix is ________. Fill in the Blank Type Question |
Question 2 Explanation:
Question 3 |
The value of x for which the matrix A =
has zero as an eigenvalue is_____.
has zero as an eigenvalue is_____. Fill in the Blank Type Question |
Question 3 Explanation:
There are 3 questions to complete.