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WorksheetsMATRIX CHALLENGE
Total questions: 30
Worksheet time: 14mins
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 -2i] is
(a)
Eigen Vectors corresponding to distinct Eigen values are
Linearly Independent
Linearly Dependent
normalized
None of the above
What is true about Hermitian matrix?
Transpose Conjugate of A = A
Transpose Conjugate of A = -A
Eigen Values are real and the Eigen vectors (for distinct Eigen values) are mutually orthogonal
Eigen Values are real but the Eigen vectors are not mutually orthogonal
What is true about Unitary Matrix?
Transpose conjugate of A = A
Modulus of each Eigen value is unity
Eigen value is +1 or -1
Transpose conjugate of A = inverse of A
Find the Eigen Values of (in increasing order)
⌈−1 0 0; 0 3 0 ; 0 0 −9 ⌉
(a)
Choose the correct options if AB=BA
A and B commutes wrt multiplication
If A is diagonal, then B is also diagonal
B=A-1
All of the above
Choose the correct options for matrix A of order 2x3
inverse of A= adjoint A / |A|
Cayley Hamilton Theorem states that A satisfies its own characteristic equation
Both of the above
None of the above
Choose the Correct Option
Every matrix commutes with its inverse
Determinant of Hermitian Matrix is Real
Diagonal Elements of Skew Hermitian Matrix is 0 or purely imaginary
All of the above
If X is the column vector of order n and A is a square matrix of order n, then what is the order of X'AX ?
1 x n
n x n
n x 1
1 x 1
A real symmetric matrix of order 3 will have ____ no. of independent components
4
6
12
8
Tell the nature of this matrix [ i i i ; i i i ; i i i]
Hermitian
Orthogonal
Skew Hermitian
Unitary
Which one is orthogonal matrix?
[ cos x sin x ; sin x cos x]
[ cos x sin x ; -sin x cos x]
[ -cos x sin x ; sin x -cos x]
[ cos x -sin x ; -sin x cos x]
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
How will you define unitary matrix A?
A' A=I
Ā' A =I
A Ā' =I
Ā' = A-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
You can post multiply a 2X3 matrix by which matrix?
There are (a) number of elements in 3x6 matrix
Which of the following can have imaginary determinant?
Hermitian
Skew Hermitian
Both
None
Choose the correct option(s)
Similar matrices have same eigen vectors
Similar matrices have same Eigen values
Diagonalizing matrix of a diagonal matrix is identity matrix
Diagonalizing matrix of a diagonal matrix is a null matrix
A system of equations will have many solutions if
no. of independent constraints is less than unknowns
no. of independent constraints is equal to unknowns
no. of independent constraints is greater than unknowns
No of independent constraints is 0
Inner Product is
a scalar quantity
a vector quantity
sometimes scalar sometimes vector
always same as a dot product
B=7 x1y1-3 x2y1+8 x1y2+10 y2x2. The matrix representation of this bilinear form is
[7 -3; 8 10]
[7 8; -3 10]
[10 -3; -8 7]
[10 8; -3, 7]
Which of them are Normal Matrix?
Hermitian
Skew Hermitian
Unitary
Real Orthogonal
Zeroth power of any matrix is
Identity matrix
Null matrix
Ones Matrix
matrix itself
Choose the correct option
exp (A) = P. exp(D). P^-1
exp (A) = P^-1 .exp(D). P
exp (A) = P^-1. P. exp(D)
P^-1 D =exp (A) P
Choose the correct option (s)
Matrix and its inverse have same eigen values
Matrix and its inverse have same eigen vectors
Matrix and its inverse is commutative wrt multiplication
Matrix and its inverse product is identity matrix provided matrix is singular
