Linear-algebra Questions Set 1:
Find the rank of the given matrix:
1 2 1
2 3 1
6 9 3
Solution:
Find the rank of the given matrix:
1 2 1
2 4 2
6 12 6
Solution:
The given matrix A is:
A = [ 1 0; 0 1 ]
Solution:
If the solutions of the quadratic equation x2 - 11x + 22 are x = 3 and x = 6, then the base of the number system is
Solution:
If A(α, β) = [cos α, sin α, 0; -sin α, cos α, 0; 0, 0, e^β], then A(α, β)^-1 is equal to:
Solution:
What is the sum and product of the eigenvalues of the given matrix?
-6 3
4 5
Solution:
Which of the following statements about orthogonal matrices are correct?
Solution:
The system of equations 4x + 6y = 8, 7x + 8y = 9, 3x + 2y = 1 has?
Solution:
Given the function f(x,y) = 4x2 + 6y2 - 8x - 4y + 8, what is the optimal value of f(x,y)?
Solution:
If P = [ √3/2 1/2 ; -1/2 √3/2 ], A = [1 1 ; 0 1] and Q = PAP', where P' is the transpose of P, then P'(Q2005)P is equal to:
Solution:
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