BME311 Spring 2022 Problem Set (release date: Feb 4th 2022) Q1 Below is the definition of vector A, B, and C, expressed by the three orthogonal unit vectors, n1, n2, and n3. Perform vector operation to answer 1A to 1D. A = 4n1 – 2n2 + n3 B = -n1 + 2n2 + 5n3 C = 2n1 – 3n2 + 6n3 (A) A·B = ? Answer: A·B = -4 -4 +5 = -3 (B) A×B = ? Answer: (C) (A×B)·C = ? Answer: (A×B)·C = -24 +63 +36 = 7 (D) A·(B×C) = ? Answer: Q2 Using the matrix a, please perform matrix operation to answer the questions below. (A) Please find the determinant of a, and also, determinant aT. Answer: det a = det aT = 40 (B) Is this matrix invertable? Answer: Yes (determinant is not zero) Q3 Please perform the matrix*vector product, which is w = Dv. Answer: 6 + 6 + 28 2 −3 4 3 40 * = = 18 + 2 + 56 6 −1 8 −2 76 −15 − 14 + 35 6 −5 7 5 7 𝑎𝑎 Q4 Please find the eigenvalues and eigenvectors for the matrix B = � −𝑎𝑎𝑎𝑎 Answer: −1 �. 𝑏𝑏