Question

Question 4 1 pts Suppose that 3 2 2 B= 2 3 -2 (Notice this is the transpose of the matrix A in the previous question.) If we wanted to find the SVD of B, we could compute the eigenvalues and eigenvectors of B" B, but this involves computing with a 3x3 matrix and might be difficult. Since we've already computed the SVD for A = B", which pieces can we reuse from the previous calculation? Hint: Pay attention to the dimensions of the matrices. The matrix Ufor B is the transpose of the matrix U that we already computed for A. The matrix 2 for Bis the transpose of the matrix that we already computed for A. The matrix V for B is the transpose of the matrix V that we already computed for A. The nonzero singular values of B are the same as the nonzero singular values of A

Answer 1

Answer: Remember to adapt this approach to the specific context and calculations you are performing, as it may vary depending on the mathematical software or tools you are using.

Step-by-step explanation: When computing the singular value decomposition (SVD) of matrix B, we can reuse several pieces from the previous calculation of matrix A's SVD. Here are the pieces that can be reused:

1. The matrix U for B is the transpose of the matrix U that we already computed for A. This means that we can directly use the transpose of U from the previous calculation for matrix B.

2. The matrix Σ for B is the same as the matrix Σ that we already computed for A. The nonzero singular values of B are the same as the nonzero singular values of A. Therefore, we can reuse the matrix Σ from the previous calculation for matrix B.

3. The matrix V for B is the transpose of the matrix V that we already computed for A. Just like with matrix U, we can directly use the transpose of V from the previous calculation for matrix B.

By reusing these pieces, we can simplify the computation of the SVD for matrix B without needing to calculate eigenvalues and eigenvectors of B" B, which can be computationally challenging for a 3x3 matrix.