List of top Data Science and Artificial Intelligence Questions on Linear Algebra asked in GATE Architecture and Planning

Select all choices that are subspaces of \(\R^3\).
Note : \(\R\) denotes the set of real numbers.

Consider the two neural networks (NNs) shown in Figures 1 and 2, with ReLU activation (ReLU(z) = max{0, z}, ∀z ∈ R). R denotes the set of real numbers. The connections and their corresponding weights are shown in the Figures. The biases at every neuron are set to 0. For what values of p, q, r in Figure 2 are the two NNs equivalent, when x₁, x₂, x₃ are positive ?

Which of the following statements is/are TRUE ?
Note: \(\R\) denotes the set of real numbers.

Let \(\R\) be the set of real numbers, U be a subspace of \(\R^3\) and M ∈ \(\R^{3×3}\) be the matrix corresponding to the projection on to the subspace U.
Which of the following statements is/are TRUE ?

Consider the directed acyclic graph (DAG) below :

Which of the following is/are valid vertex orderings that can be obtained from a topological sort of the DAG ?