Apply row operations and cofactor expansions to calculate 1 127 1 2-α -23 28 det 2...
a)Use row reduction and/or cofactor expansion to calculate the determinant of c) Calculate the following determinants, using your answer to part a det(A^−1 ) det(2A) det(A^2 ) det(A^T A) 3 3 3 -1 2 2 A= 1 9 6 2 2 2 4 2
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) Let A- be an arbitrary 2 x 2 matrix. (a) If A is invertible, perform row operations to determine a row echelon form of A. (Hint: You may need to consider different cases, e.g., when a-0 and when a f 0.) (b) Under certain conditions, we can row reduce [A | 2 to [| B] where d -b ad- be-a Use the row echelon form of A from part (a) to find conditions under which the...
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?...
Question 23 (1 point) Let o A = 3 1 Which of the following computes det(A) using the cofactor expansion along the third column? 2) 3 --) 1 +23 +2 이. o (3) 2 23 의
These are linear algebra problems. 1 4 1 1 2 7 2 2 Let A 1 4 .. 1 2 find Its Inverse. Decide whether the matrix A is invertible, and if so, use the adjoint method Enter as a matrix, exactly in fractional from if required, if not invertible enter "NA" A-1 la b -2a -2b -2c d e f d = -2,find Given that g hi g-3d h-3e -3f -2a -2b -2c d f g 3d h 3e...
(1 point) Perform one step of row reduction, in order to calculate the values for x and y by back substitution. Then calculate the values for x and y. Also calculate the determinant of the original matrix. (Note: since the determinant is unchanged by type 3 row operations, it will be easier to calculate the determinant of the row reduced matrix.) (12 32] [31 = [1] det =
please provide detailed and clear solutions for the following 2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coumn expansions or elementary row operations and the properties of determinants). Are A and B invertible? Calculate their inverses if they exist 1b. Are the columns of A linearly dependent or linearly independent? Find the dimension of Nul A and the rank of A. What can you say about the number of...
Calculate the determinant using cofactor expansion along any row or column. 1 0 3 1 1 1 -3 3 1 1 2 2 6 0 (a) 2 0 6 (b) -4 -2 -5 -1 0 -3 1 1 -1 5 2 2 5 4 1 12 0
Explain all parts of question 1 and question 2 in detail 1. Consider the matrix In + Inn, which has every diagonal entry equal to 2 and every off-diagonal entry equal to 1. (a) Compute det(In + Inn) for each of n = 1,2,3. (b) For n = 4, we have 2 1 1 1 1 2 1 1 1 1 2 1 111 2 2 1 1 1 -1 1 0 0 -1 0 1 0 -1 0 0...