MCQ Bank
If B=\[\{ {v_1},{v_2},{v_3}\} \] is an orthogonal set of vectors with respect to an inner product on a vector space V, then the set B
- A) Is linearly independent.
- B) Is an orthonormal basis for v
- C) Spans the vector space v
- D) Linearly dependent.
A matrix [A]_{n \times n has both positive and negative eigenvalues so in this case origin behaves as a --------------
- A) Critical point
- B) Saddle point
- C)
- D)
Let \[s = \{ {u_1} + {u_2} + ......{u_p}\} \] be the set of non-zero vectors in \[{R^n}\] is said to be an orthogonal set if all vectors in S are mutually orthogonal. That is O∉ S and \[{u_i}.{u_j} = 0\,\] ∀ i≠ j, i,j=1,2,……..p.
- A) False
- B) True
- C)
- D)
The norm of v is the non-negative scalar||v|| defined by
- A) ||v||=\sqrt{v_{1}^{2}+v_{2}^{2}+...v_{n}^{2}}
- B) ||v||=v_{1}^{2}+v_{2}^{2}+...v_{n}^{2}
- C)
- D)
If A and B are row equivalent matrices, then (a) A given set of column vectors of A is ¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬¬_______________if and only if the corresponding column vectors of B are __________________.
- A) Linearly independent, linearly independent
- B) Linearly independent, linearly dependent
- C) Linearly dependent, linearly dependent
- D) Linearly dependent, linearly independent
Eigenvector(s) of the matrix \[\left[ {\begin{array}{*{20}{c}} 0&0&a \\ 0&0&0 \\ 0&0&0 \end{array}} \right]\] is (are):
- A) (0, a, 0)
- B) None of the above
- C) (0, 0, 1)
- D) (0, 0, a)