Explain all parts of question 1 and question 2 in detail 1. Consider the matrix In...
Determinants and linear transformations 4. (a) Let A be the matrix 1 -2 4 1 3 2 11 i) Calculate the determinant of A using cofactor expansion of row 3. (ii) Is A invertible? If so, give the third column of A1 (you do not have to simplify any fractions) (b) Let B be the matrix 0 0 4 0 2 8 0 4 2 1 0 0 0 7 Use row operations to find the determinant of B. Make...
2 invertible? C For which values of c is the matrix 8 O c 4 c =-4 Both of the above, i.e., c +4 Neither of the above, i.e., c +4. Suppose that the following row operations: interchange rows 1 and 3 multiply row 3 by 1/2 add -3 times row 1 to row 2 2 1 7 in this order, transform a matrix A into B = | 0 4-5 L0 0 3 What is the determinant of A?...
21/le/content/352479/viewContent/3310368/View?ou = 352479 1020 1050 1040 St. John's, NL - 7 Da... MEMORIAL UNIVERSITY OF NEWFOUNDLAND DEPARTMENT OF MATHEMATICS AND STATISTICS © Solomon Assignment 8 Mathematics 2050 Spring 2020 Due: July 30, 2020, 11:59 pm . SHOW ALL WORK a b c -T (3) 1. If pg T -1, compute 3p+a 3q+b3r + 2p 24 2r [2] [2] 2. (a) What are the possible values of det(A) if A-' = A' ? (b) A matrix is skew symmetric if A"...
Differention Equations - Can someone answer the checked numbers please? Determinants 659 is the characteristic equation of A with λ replaced by /L we can multiply by A-1 to get o get Now solve for A1, noting that ao- det A0 The matrix A-0 22 has characteristic equation 0 0 2 2-A)P-8-12A +62- 0, so 8A1-12+6A -A, r 8A1-12 Hence we need only divide by 8 after computing 6A+. 23 1 4 12 10 4 -64 EXERCISES 1. Find AB,...
Let A and B be nxn matrices. Mark each statement true or false. Justify each answer. Complete parts (a) through (d) below. a. The determinant of A is the product of the diagonal entries in A. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The statement is false because the determinant of the 2x2 matrix A = is not equal to the product of the entries on the main...
True or False? 1. If σ is a singular value of a matrix A, then σ is an eigenvalue of ATA Answer: 2. Every matrix has the same singular values as its transpose Answer: 3. A matrix has a pseudo-inverse if and only if it is not invertible. Answer: 4. If matrix A has rank k, then A has k singular values Answer:_ 5. Every matrix has a singular value decomposit ion Answer:_ 6. Every matrix has a unique singular...
1. To prove the theorem in detail. Theorem: det A for any n X n-matrix A can be computed by a cofactor expansion across the ith row of A, that is, det A H-1)adtAj Hint: Use induction on i, For the induction step from i to i+1, flip rows i and i+1 (How does this change the determinant?) and use the induction assumption. 1. To prove the theorem in detail. Theorem: det A for any n X n-matrix A can...
QUESTION 3 1 points Which property of determinants is illustrated by the equation 8 8 l1 1 87 8 7 O a. If every entry of an n Xn matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. O b. If a single row or a single column of an n Xn matrix is multiplied by a constant c, then the determinant of the matrix is multiplied by c. O c. If...
Review 4: question 1 Let A be an n x n matrix. Which of the below is not true? A. A scalar 2 is an eigenvalue of A if and only if (A - 11) is not invertible. B. A non-zero vector x is an eigenvector corresponding to an eigenvalue if and only if x is a solution of the matrix equation (A-11)x= 0. C. To find all eigenvalues of A, we solve the characteristic equation det(A-2) = 0. D)....
Let A be an n×n matrix. Mark each statement as true or false. Justify each answer. a. An n×n determinant is defined by determinants of (n−1)×(n−1) submatrices. b. The (i,j)-cofactor of a matrix A is the matrix obtained by deleting from A its I’th row and j’th column. a. Choose the correct answer below. A. The statement is false. Although determinants of (n−1)×(n−1)submatrices can be used to find n×n determinants,they are not involved in the definition of n×n determinants. B....