Assignment No.
:2
Max. Marks: 12
Group A
Sr. No. Question
1. For what values of λ and µ do the system of equations
x+y+z=6,x+2y+3z=10,x+2y+λz=µ have
a) no solution b) unique solution c) more than one solution.
2 1 1
2. −3 3 3
2 2 1
Prove that the matrix 3 3 3
is orthogonal
1 −2 2
[ 3 3 3]
3. −2 2 −3
Diagonalize the matrix A =[ 2 1 −6] and obtain its modal
−1 −2 0
matrix.
4.
Evaluate the following limit if it exists
Group B
Sr. No. Question
1. Reduce the following matrices to the Normal form and hence find their
1 2 −1 4
ranks [ 2 4 3 4 ]
1 2 3 4
−1 −2 6 −7
2. Test the consistency & Solve
5x + 3y + 7z = 4
3x + 26y + 2z = 9
7x + 2y + 11z = 5
3. cos 𝜃 0 sin 𝜃
Verify that the matrix A = [ 0 1 0 ] is
sin 𝜃 0 cos 𝜃
orthogonal or not.
4.
Solve
Group C
Sr. No. Question
1. Discuss the consistency of the following system of equations.
X+2y+3z=0 ,3x+4y+4z=0 ,7x+10y+12z=0
2. Find rank of the following matrix A =
−1 2 3 −2
[ 2 −5 1 2]
3 −8 5 2
5 −12 −1 6
3.
Find the limit if exists,
4. Are the following vectors L.D. if so find the relation
between them (2,1,1), (2,0, −1), (4,2,1)
Group D
Sr. No. Question
1. Test for Consistency and hence solve
x+y+z=9
2x + 5y +7z = 52
2x + y – z =0
1 2 3
2. Show that column vectors of the matrix A=[−2 1 2
] are linearly
dependent
3. Show that matrix A is not diagonalizable
1 2 2
A=[ 0 2 1]
−1 2 2
4.
Find
Group E
Sr. No. Question
1. For what value of K will the following equation fail to have unique
solution.
3x-y+Kz=1
2x+y+z=2
x+2y-Kz=-1 will the equation have any solution for these
values of K?
2. find the inverse of the matrix Using gauss Jordan method
−1 2 2
A= [ 2 −1 2 ]
2 2 −1
3. Determine the Rank of the following matrix
1 3 4 5
[1 2 6 7]
1 5 0 10
4.
Find , if it exists.
Group F
Sr. No. Question
1. Find the Eigen Values and Eigen Vectors of the matrices
8 −6 2
A=[−6 7 −4]
2 −4 3
2. Reduce the matrix to normal form and hence find their rank.
8 1 3 6
A=[ 0 3 2 2]
−8 −1−3 4
3.
Find
4. Test for Consistency and hence solve
x+y+z=9
2x + 5y +7z = 52
2x + y – z =0
Group G
Sr. No. Question
1. Find the eigen value and eigen vector of the matrix A
1 1 3
A=[1 5 1]
3 1 1
2. If A is hermitian matrix then prove that iA is a skew- hermitian
3. Find the sum and product of eigen value of matrix A
3 1 4
A=[0 2 6]
0 0 5
4.
Find
Group H
Sr. No. Question
1. .Find P such that 𝑃 −1 𝐴𝑃 is diagonal matrix
3 1 −1
A=[−2 1 2 ]
0 1 2
2. 𝑒𝑥
Evaluate the limit if exists, lim
𝑥→∞ 𝑥 3
3. −1 2 −2
Reduce the Matrix to diagonal form,A=[ 1 2 1]
−1 −1 0
4. Show that every square matrix is expressible as the sun of a
Hermitian matrix and a skew-hermitian matrix.
Group I
Sr. No. Question
1. 1 1 𝑘
Find the value of k so that the vectors [−1], [ 2 ] and [0] are
3 −2 1
linearly dependent.
2. 1 1 2
For the matrix A = [1 2 3 ] , Find non – singular matrices P&
0 −1 −1
Q such that PAQ is in the normal form.
3. −2 2 −3
Diagonalize the matrix A =[ 2 1 −6] and obtain its modal
−1 −2 0
matrix.
4.
Evaluate the following limit:
Group J
Sr. No. Question
1. Test the consistency and solve 2x-3y+7z=5
3x+y-3z=13
2x+19y-47z=32.
2.
Evaluate the following limit:
3. Find the latent root and latent vector of the matrix A
2 1 −1
A=[ 1 1 −2]
−1 −2 1
4. 1. Use Gauss Jordan method to find the inverse of the matrix.
2 1 −1
A=[0 2 1]
5 2 −3
