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GATE20 Engg. Mathematics Series: Linear Algebra Quiz 4 (App update required to attempt this test)
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Question 1
Consider the following linear system.
This system is consistent if a,b and c satisfy the equation
This system is consistent if a,b and c satisfy the equation
Question 2
Two eigen values of a real matrix P are and 3. The determinant of P is _________.
Question 3
In the given matrix one of the Eigen values is 1. The Eigen vectors corresponding to the Eigen value1are
Question 4
The product of the non-zero eigenvalues of the matrix
is _____.
is _____.
Question 5
Consider a 3×3 real symmetric matrix S such that two of its eigenvalue are a≠0, b≠0 with respective eigenvectors . If a≠b then x1y1 + x2y2 + x3y3 equals
Question 6
Consider the matrix
Which one of the following statements about P is INCORRECT?
Which one of the following statements about P is INCORRECT?
Question 7
For the matrix ONE of the normalized eigen vector is given as
Question 8
The system of equations
x + y + z = 6
x + 4y + 6z = 20
x + 4y + λz = µ
has NO solution for values λ and µ given by
x + y + z = 6
x + 4y + 6z = 20
x + 4y + λz = µ
has NO solution for values λ and µ given by
Question 9
An eigen vector of P = is
Question 10
Given that
and , the value of A3 is
and , the value of A3 is
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