Given A be a matrix.
then must be a matrix of inverse order of A . thus order of is .
Thus,
So, size of .
Similarly,
So, size of
Thus, both is defined.
(5) Let A be some 4 x 6-matrix. Explain why AAT and AT A are defined....
4. Let A be a square matrix such that AAT-1. Show that AI = ±1. 4. Let A be a square matrix such that AAT-1. Show that AI = ±1.
Find ATA and AAT for the following matrix. 4-1-4-6 31 2 -5 4 AAT = What do you observe? This answer has not been graded yet.
Let A be a matrix of size m xn. Show that AAT and AT A are both square matrices (equal number of rows and columns) (10 pts) If A is mXn then A is nXm so AA must have size mXm Similarly, A" A must be nxn
I need help with this question. Some clarification would be great. 3. Consider the following matrix A= 3 6 (a) Compute AAT and its eigenvalues and unit eigenvectors. (b) Find the SVD by computing the matrices U, V, Σ 3. Consider the following matrix A= 3 6 (a) Compute AAT and its eigenvalues and unit eigenvectors. (b) Find the SVD by computing the matrices U, V, Σ
Let A and E be matrices with the following sizes.A: 3 × 4 E: 4 × 3 If defined, determine the size of the matrix E − 2A. (If an answer is undefined, enter UNDEFINED.) × If not defined, explain why. E − 2A is defined. E − 2A is not defined because E and 2A have different sizes. E − 2A is not defined because E and 2A have the same size. E − 2A is not defined because the...
2. Partitioned matrices A matrix A is a (2 x 2) block matrix if it is represented in the form [ A 1 A2 1 A = | A3 A4 where each of the A; are matrices. Note that the matrix A need not be a square matrix; for instance, A might be (7 x 12) with Aj being (3 x 5), A2 being (3 x 7), A3 being (4 x 5), and A4 being (4 x 7). We can...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det (A?)? (d) (4 points) What is det(A-?)? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of AT are linearly independent. and 2 6. (6 points) Let...
4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(AT)? (d) (4 points) What is det(A-')? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of A™ are linearly independent. and t = [ ] 6. (6...
Matrix Methods/Linear Algebra: Please show all work and justify the answer! 4. Let A and B be 4 x 4 matrices. Suppose det A = 4 and det(AB) = 20. (a) (4 points) What is det B? (b) (4 points) Is B invertible? Why or why not? (c) (4 points) What is det(A”)? (d) (4 points) What is det(A-")? 5. (6 points) Let A be an n x n invertible matrix. Use complete sentences to explain why the columns of...
6 7. Let A be a 4 x 4 matrix. The eigenvectors of A are 6 and –5. The eigenspace corresponding to 1 = 6 is 2-dimensional and the eigenspace corresponding to 1 = -5 is 1-dimensional. Is A diagonalizable? Why or why not?