Given the matrix the eigenvector is
The eigen values and the corresponding eigen vectors of a 2 × 2 matrix are given by
We know, sum of eigen values = trace (A). = Sum of diagonal element of A.
Therefore λ1 + λ 2 = 8 + 4 =12
Option (a)gives, trace(A) = 6 + 6 =12.
All the four entries of the 2 × 2 matrix are nonzero, and one of its eigen values is zero. Which of the following statements is true?
One eigen value is zero
The eigen values of the following matrix are
Let the matrix be A. We know, Trace (A)=sum of eigen values.
The three characteristic roots of the following matrix A
A is lower triangular matrix. So eigen values are only the diagonal elements.
The sum of the eigenvalues of the matrix given below is
Sum of eigen values of A= trace (A)
For which value of x will the matrix given below become singular?
Let the given matrix be A. A is singular.
Eigen values of a matrix are 5 and 1. What are the eigen values of the matrix S2 = SS?
We know If λ be the eigen value of A ⇒λ2 is an eigen value of A2 .
The number of linearly independent eigenvectors of
Number of linear independent vectors is equal to the sum of Geometric Multiplicity of eigen values. Here only eigen value is 2. To find Geometric multiplicity find n-r of (matrix-2I), where n is order and r is rank. Rank of obtained matrix is 1 and n=2 so n-r=1. Therefore the no of linearly independent eigen vectors is 1
The eigenvectors of the matrix are written in the form . What is a + b?
One of the Eigenvectors of the matrix A = is
The eigen vectors of A are given by AX= λ X
So we can check by multiplication.
The minimum and the maximum eigen values of the matrix are –2 and 6, respectively. What is the other eigen value?
The state variable description of a linear autonomous system is, X= AX,
Where X is the two dimensional state vector and A is the system matrix given by
The roots of the characteristic equation are
Characteristic equation will be :λ2 -4 =0 thus root of characteristic equation will be +2 and - 2.
For the matrix s one of the eigen values is equal to -2. Which of the following is an eigen vector?
x=[x1x2…..xn]T is an n-tuple nonzero vector. The n×n matrix V=xxT
As every minor of order 2 is zero.
Cayley - Hamiltion Theorem states that square matrix satisfies its own characteristic equation, Consider a matrix
If the rank of a (5×6) matrix Q is 4, then which one of the following statements is correct?
Rank of a matrix is equal to the No. of linearly independent row or no. of linearly independent column vector.
The trace and determinate of a 2 ×2 matrix are known to be – 2 and – 35 respectively. Its eigenvalues are
Identify which one of the following is an eigenvector of the matrix
Eigen Value (λ ) are 1,− 2.
be the eigen of A. Corresponding
To λ then.
be the eigen vector corrosponding to λ = 1
The eigenvalues of
If upper triangular or lower triangular matrix are given then trace of matrix is equal to eigen value.