List of top Statistical Science Questions on Linear Algebra

Which of the following statement is true?

Let \(A\) be a \(5 \times 5\) skew-symmetric matrix, then the determinant of \(A\) is:

Let \(A = \begin{bmatrix} 2 & 1 & 4 3 & 2 & 5 0 & -1 & 1 \end{bmatrix}\) be a matrix, then the rank of \(A\) is:

Let \(A\) be an \(n \times n\) matrix of real number such that \(A^2 = A\), then the Eigen values \(A\) are:

The solution of the system of equations
\[ x_1 - 3x_2 + 4x_3 = 3 \]
\[ 2x_1 - 5x_2 + 7x_3 = 6 \]
\[ 3x_1 - 8x_2 + 11x_3 = 11 \]
is given by:

Let \[ a_n=\frac{\sin n}{n} \] be a sequence of real numbers. Then, \[ \lim_{n\to\infty} a_n \] is

Let \(3x + 2iy - ix + 5y = 7 + 5i\), then values of \(x\) and \(y\) respectively are given by

The equation of conic section whose vertices are \((0, \pm 8)\) and asymptotes are \(y = \pm \frac{4}{3}x\) is given by

The series \(\sum_{n=1}^\infty a_n = \sum_{n=1}^\infty \frac{1}{n^2}\) and \(\sum_{n=1}^\infty b_n = \sum_{n=1}^\infty \frac{1}{n^3}\) are

For what value of \(p\), the series \(\sum_{n=1}^\infty \frac{1}{n^p}\) is convergent

The formula to solve simple non-linear equation f(x) = 0 by Newton’s Raphson Method is given by :

In the straight line graph of the linear equation Y = a + bX, slope is horizontal if :

Let \(\mathbb{R}^n = V\) is a vector space over the field of real numbers, then which of the following is a subspace ?

Let A = \(\begin{bmatrix} 1 & 2 & 0 & -1 2 & 6 & -3 & -3 3 & 10 & -6 & -5 \end{bmatrix}\) , then rank of matrix A is :

Let \(W_1\) and \(W_2\) are two subspaces of a vector space V over the field F, then :

Let B = \(\begin{bmatrix} 5 & -9 & 6 0 & 2 & 3 0 & 0 & 7 \end{bmatrix}\) , then its reduced echelon form is :

Let A and B be two invertible matrices, then which of the following is true ?

Let A and B be two matrices and \(\gamma\) be any scalar, then :

The number of common tangents to the circles $x^2 + y^2 - 6x - 14y + 48 = 0$ and $x^2 + y^2 = 6x$ is :

The sequence given by $a_1 = \frac{3}{2}, a_{n+1} = 2 - \frac{1}{a_n} \quad \forall n \ge 1$ :

The series $\sum_{n=2}^{\infty} a_n$, where the $n^{th}$ term is $a_n = \frac{1}{\log n}$ :

The series $\sum_{n=1}^{\infty} \frac{x^n}{n+1}$ is :

The equation of second degree $2x^2 - 3xy - py^2 + x + qy - 1 = 0$ represents 2 mutually perpendicular straight lines if :

If an n x n matrix A satisfies the equation \(A^2 - 2A + I = 0\), then:
1. \(A^3 = 3A - 2I, A^4 = 4A - 3I\)
2. \(A^3 = 2A - I, A^4 = 4A - 3I\)
3. \(A^3 = 2A^2 - 3I, A^4 = 3A^2 - 4I\)
4. \(A^3 = 4A - 3I, A^4 = 3A - 2I\)

If \(A = \begin{pmatrix} 2 & 3 1 & 2 \end{pmatrix}\), then \(A^{-1}\) is: