Eigen Value and Eigen vector , Differentiation

If the eigen values of 3X3 matrix is 2,5,3 then find detA

• 30

• 40

• 50

• 20

Which one is the characteristic equation ?

• [ A-mI ] = 0

• | A-mI | = 0

• AX =mX

• | A | X= mX

Choose the Correct Options

• Sum of the Diagonal Elements of A=Trace of transpose of A

• Sum of the Diagonal Elements of A=Trace of the Eigen value Diagonal matrix D

• Sum of the Eigen Values of A=Trace of A

• Sum of the Eigen Values of A=Determinant of A

What is true about singular matrix A?

• |A| is 0

• |A| is not 0

• Atleast one of the Eigen Value if 0 implies its singularity

• Its inverse do not exist

Norm of the Row matrix A=[1 2 2] is

(a)  

Eigen Vectors corresponding to distinct Eigen values are

• Linearly Independent

• Linearly Dependent

• normalized

• None of the above

If A and B are the two Eigen vectors, then the condition for their orthogonality is

• B Ā'=0

• Ā' B=0

• Ā' B=1

• B Ā'=1

What is the trace of A= [ 2 3 6 ; -9 0 8 ; 6 2 3]

• 5

• 4

• -4

• -5

Classify the matrix  

• Square matrix,  Diagonal matrix

• Idempotent matrix, Diagonal matrix

• Square matrix, Identity matrix

• Square matrix, triangular matrix

If the sum of two eigen values and trace of a 3 x 3 matrix are equal then the determinant value of the matrix is ________

• 1

• 0

• -1