Question 2: Using the file "transformations.xlsx" available at https://drive.google.com/drive/u/1/folders/1A2B3C4D5E6F7G8H910J, each matrix provided represents a bounded linear operator on a finite-dimensional vector space. Instructions: 1. Download the file and review the list of matrices, each labeled with their respective vector space dimensions. 2. Let T represent a transformation matrix from the file. Answer the following questions based on T: a) Prove whether the operator norm of T is bounded, and calculate it for a matrix of your choice. Describe each step and the principles behind your calculation. b) Consider a transformation matrix T that represents a compact operator on a Hilbert space. Demonstrate whether or not I could have an infinite number of non-zero eigenvalues. Use an example from the dataset and explain how this applies within the concept of compact operators. c) For a matrix T in the dataset with eigenvalues given in "eigenvalues.txt," calculate the trace of T and verify if it corresponds to the sum of its eigenvalues. If there is a discrepancy, explain why, based on the properties of T. Use appropriate theorems and provide a clear, detailed solution.

Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.

Show that the matrix below does not have an LU factorization. A=0110

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The sequence of numbers we’re generating are traditionally constructedlike this: Start with the first 2 numbers. To get the next number, take the 2most recent numbers and add them together to get the next one.Explain why our matrix vector multiplication is generating the same numbersas the traditional procedure.

If the null space of a 30x17 matrix is 13-dimensional, find the rank of the matrix.

and u = Write y as the sum of two orthogonal vectors, one in Span {u} and one orthogonal to u. Let y = (Type an integer or simplified fraction for each matrix element. List the terms in the same order as they appear in the original list.) Enter your answer in each of the answer boxes