# Linear Algebra 1 marks

GATE 2019 Set-1

1. Consider the matrix
P = $$\large \begin{bmatrix} 1 & 1 & 0\\ 0 & 1 & 1\\ 0 & 0 & 1 \end{bmatrix}$$
The number of distinct eigenvalues of P is

(A) 0

(B) 1

(C) 2

(D) 3

GATE 2019 Set-2

1. In matrix equation [ ]{ } = { } ,

] = $$\begin{bmatrix} 4 & 8 & 4\\ 8& 16 & -4\\ 4 & -4 &15 \end{bmatrix}$$,{ }= $$\begin{Bmatrix} 2\\ 1\\ 4\end{Bmatrix}$$ and { } = $$\begin{Bmatrix} 32\\ 16\\ 64\end{Bmatrix}$$

One of the eigenvalues of matrix [A] is

(A) 4

(B) 8

(C) 15

(D) 16

2. The transformation matrix for mirroring a point in x – y plane about the line y = x is given by

(A) $$\begin{bmatrix} 1 & 0\\ 0& -1 \end{bmatrix}$$

(B) $$\begin{bmatrix} -1 & 0\\ 0& 1 \end{bmatrix}$$

(C) $$\begin{bmatrix} 0 & 1\\ 1& 0 \end{bmatrix}$$

(D) $$\begin{bmatrix} 0 & -1\\ -1& 0 \end{bmatrix}$$

GATE 2018 Set-1

1. The rank of the matrix $$\large \begin{bmatrix} -4 & 1 &-1 \\ -1& -1& -1\\ 7& -3& 1 \end{bmatrix}$$ is

(A) 1

(B) 2

(C) 3

(D) 4

GATE 2018 Set-2

1. If A = $$\begin{pmatrix} {1} & {2} & {3}\\ {0} & {4} & {5}\\ {0} & {0} & {1} \end{pmatrix}$$ then det($$A^{-1}$$) is __________ (correct to two decimal places).

GATE 2017 Set-1

1. The product of Eigen values of the matrix P is $$\large P=\begin{bmatrix} 2 & 0&1 \\ 4& -3 & 3\\ 0&2 & -1 \end{bmatrix}$$

(A) -6

(B) 2

(C) 6

(D) -2

GATE 2017 Set-2

1. The determinant of a 2×2 matrix is 50. If one eigenvalue of the matrix is 10, the other eigenvalue is ___________

GATE 2016 Set-1

1. The solution to the system of equations $$\large \begin{bmatrix} 2 &5 \\ -4& 3 \end{bmatrix}\begin{bmatrix} x\\y \end{bmatrix}=\begin{bmatrix} 2\\-30 \end{bmatrix}$$ is

(A) 6,2

(B) -6,2

(C) -6,-2

(D) 6,-2

GATE 2016 Set-2

1. The condition for which the eigenvalues of the matrix
$$\large \begin{bmatrix} 2 &1 \\ 1& k \end{bmatrix}$$

are positive, is

(A) k > 1/2

(B) k > −2

(C) k > 0

(D) k < −1/2

GATE 2016 Set-3

1. A real square matrix A is called skew-symmetric if

(A) AT = A

(B) AT = A-1

(C) AT = -A

(D) AT = A + A-1

GATE 2015 Set-1

1. If any two columns of a determinant P=$$\large \begin{bmatrix} 4 &7 &8 \\ 3&1 &5 \\ 9&6 &2 \end{bmatrix}$$are interchanged, which one of the following statements regarding the value of the determinant is CORRECT?

(A) Absolute value remains unchanged but sign will change.

(B) Both absolute value and sign will change.

(C) Absolute value will change but sign will not change.

(D) Both absolute value and sign will remain unchanged.

GATE 2015 Set-2

1. At least one eigen value of a singular matrix is

(A) positive

(B) zero

(C) negative

(D) imaginary

1. The lowest eigenvalue of the 2×2 matrix $$\large \begin{bmatrix} 4 &2 \\ 1&3 \end{bmatrix}$$ is ____