Question 1 |

Let A be the adjacency matrix of the graph with vertices {1, 2, 3, 4, 5}.

Let \lambda _1,\lambda _2,\lambda _3,\lambda _4,\; and \; \lambda _5 be the five eigenvalues of A. Note that these eigenvalues need not be distinct.

The value of \lambda _1+\lambda _2+\lambda _3+ \lambda _4+ \lambda _5 = _____

Let \lambda _1,\lambda _2,\lambda _3,\lambda _4,\; and \; \lambda _5 be the five eigenvalues of A. Note that these eigenvalues need not be distinct.

The value of \lambda _1+\lambda _2+\lambda _3+ \lambda _4+ \lambda _5 = _____

1 | |

2 | |

3 | |

4 |

Question 1 Explanation:

Question 2 |

Let A=\begin{bmatrix}
1 & 2 & 3 &4 \\
4& 1& 2 &3 \\
3& 4 & 1 &2 \\
2 &3 &4 &1
\end{bmatrix} and B=\begin{bmatrix}
3& 4 & 1 &2 \\
4& 1& 2 &3 \\
1 & 2 & 3 &4 \\
2 &3 &4 &1
\end{bmatrix}

Let det(A) and det(B) denote the determinants of the matrices A and B, respectively.

Which one of the options given below is TRUE?

Let det(A) and det(B) denote the determinants of the matrices A and B, respectively.

Which one of the options given below is TRUE?

det(A) = det(B) | |

det(B) = - det(A) | |

det(A)=0 | |

det(AB) = det(A) + det(B) |

Question 2 Explanation:

Question 3 |

Which of the following is/are the eigenvector(s) for the matrix given below?

\begin{pmatrix} -9 &-6 &-2 &-4 \\ -8& -6 & -3 & -1 \\ 20 & 15 & 8 & 5 \\ 32& 21& 7&12 \end{pmatrix}

\begin{pmatrix} -9 &-6 &-2 &-4 \\ -8& -6 & -3 & -1 \\ 20 & 15 & 8 & 5 \\ 32& 21& 7&12 \end{pmatrix}

**MSQ**\begin{pmatrix}
-1\\
1\\
0\\
1
\end{pmatrix} | |

\begin{pmatrix}
1\\
0\\
-1\\
0
\end{pmatrix} | |

\begin{pmatrix}
-1\\
0\\
2\\
2
\end{pmatrix} | |

\begin{pmatrix}
0\\
1\\
-3\\
0
\end{pmatrix} |

Question 3 Explanation:

Question 4 |

Consider solving the following system of simultaneous equations using LU decomposition.

\begin{aligned} x_1+x_2-2x_3&=4 \\ x_1+3x_2-x_3&=7 \\ 2x_1+x_2-5x_3&=7 \end{aligned}

where L and U are denoted as

L= \begin{bmatrix} L_{11} & 0 & 0 \\ L_{21}& L_{22} & 0 \\ L_{31} & L_{32} & L_{33} \end{bmatrix}, U= \begin{bmatrix} U_{11} & U_{12} & U_{13} \\ 0& U_{22} & U_{23} \\ 0 & 0 & U_{33} \end{bmatrix}

Which one of the following is the correct combination of values for L32, U33, and x_1?

\begin{aligned} x_1+x_2-2x_3&=4 \\ x_1+3x_2-x_3&=7 \\ 2x_1+x_2-5x_3&=7 \end{aligned}

where L and U are denoted as

L= \begin{bmatrix} L_{11} & 0 & 0 \\ L_{21}& L_{22} & 0 \\ L_{31} & L_{32} & L_{33} \end{bmatrix}, U= \begin{bmatrix} U_{11} & U_{12} & U_{13} \\ 0& U_{22} & U_{23} \\ 0 & 0 & U_{33} \end{bmatrix}

Which one of the following is the correct combination of values for L32, U33, and x_1?

L_{32}=2,U_{33}=-\frac{1}{2},x_1=-1 | |

L_{32}=2,U_{33}=2,x_1=-1 | |

L_{32}=-\frac{1}{2},U_{33}=2,x_1=0 | |

L_{32}=-\frac{1}{2},U_{33}=-\frac{1}{2},x_1=0 |

Question 4 Explanation:

Question 5 |

Consider the following two statements with respect to the matrices A_{m \times n},B_{n \times m},C_{n \times n} \text{ and }D_{n \times n},

Statement 1: tr(AB) = tr(BA)

Statement 2: tr(CD) = tr(DC)

wheretr() represents the trace of a matrix. Which one of the following holds?

Statement 1: tr(AB) = tr(BA)

Statement 2: tr(CD) = tr(DC)

wheretr() represents the trace of a matrix. Which one of the following holds?

Statement 1 is correct and Statement 2 is wrong. | |

Statement 1 is wrong and Statement 2 is correct. | |

Both Statement 1 and Statement 2 are correct. | |

Both Statement 1 and Statement 2 are wrong. |

Question 5 Explanation:

There are 5 questions to complete.

Please make a login portal, so we can track our progress

Dear Chinmay Rajpurohit,

We will consider your suggestion.

Agree

Agreed

Hey Team,

Linear Algebra

In Q1 from Gate 2022 Option C should be [-1 0 2 2]ᵀ

Option “C” given in Gate 2022 for MSQ is wrong it should be {-1 0 2 2}^T Kindly Look Into it.

Dear Raghav,

We have updated the option.

Thank You.

Question no. 74

Value of matrices a13 = -4 not -1 , Please verify and correct it\

Question updated with value -4.

Question no. 79 some coding error . please click on correct option and check the error.

Answer Updated.

Question no. 22

Please remove ? marks from its create confusion.

Question text updated.

please update question 31 cuz in the 6th line you’ve done A[j][i] = temp ? c which is originally temp -c

Question updated for GATE CSE 2014 SET-3.

Plz upload mock test for other subject also