Engineering Mathematics
Linear Algebra
Practice questions from Linear Algebra.
8
Total0
Attempted0
Correct0
IncorrectConsider the set of points which minimize the real valued function
Which of the following statements is true about the set S?
Thus,
Calculating stationary points:
Let
Let
where is an arbitrary constant.
Thus, these are infinitely many stationary points.
Option (b) is correct.
Let and be the two eigenvectors corresponding to distinct eigenvalues of a real symmetric matrix. Which one of the following statements is true?
The eigen vectors of a real symmetric matrix corresponding to different eigen values are always pair-wise orthogonal.
So, for the given two eigen vectors and ,
option (B) is correct.
Let , and . Then, the system of linear equations has
will have an infinite no. of solutions
Option (b) is correct.
Let and let I can be identity matrix. Then is equal to
Option (a) is correct.
Which one of the following matrices has an inverse?
If any matrix has one or more rows that are linearly dependent on other rows then determinant is 0
Let us check options Where determinant
(a) determinant
(b) determinant
(c) all rows are linearly independent
determinant
(d) determinant
The sum of the eigenvalues of the matrix is ________ (rounded off to the nearest integer).
The eigenvalues of the matrix raised to a certain power is eigenvalue raised to that same power.
For a given vector , the vector normal to the plane defined by is
Equation of plane in 3D:
Vector normal to plane is given by
In the figure, the vectors and are related as: by a transformation matrix A. The correct choice of is
is CW rotation of by 36.86°
For rotation of a vector by an angle θ in anti-CW direction matrix used.
When vector is to be rotated CW, we use negative value of θ.
θ = -36.86°, cos θ = 0.8, sin θ = -0.6
matrix
