Question 23 (1 point) Let o A = 3 1 Which of the following computes det(A)...
(1 point) Let A= 1-1 -3 -37 6 23 22 (4 128] (a) Compute det(A) = (b) Use Cramer's rule to solve the following system { 1 - - 312 611 + 237 401 + 12 + + 313 = 22+ = 8) = 5 -1 2
els response. Let B -- [1 1 L2 2. 0 1 31 2. Find det B 1 (a) via reduction to triangular form (b) by cofactor expansion swer) in the textbox below. Only work on your blank sheets of paper. You will submit your 3 (12pt) - T-
Given that A is the matrix 5-3 1 1-5 7 6 3 –77 -4 -5] The cofactor expansion of the determinant of A along column 1 is: det(A) = a1 · |A1| + a2 · |A2| + az · |A3|, where a1 = num @ az = numi @ a3 = num @ and A2 = Thus det(A) = num
Apply row operations and cofactor expansions to calculate 1 127 1 2-α -23 28 det 2 22 19 For which α is the matrix invertible?
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...
Question 3 (1 point) Which of the following statements are true? If one row of a matrix is a linear combination of two other rows, then the determinant is 0. If the determinant of an nxn matrix is not zero, then the columns span the entire Rn The determinant is linear in each column. The row operation R2-R1-R2 (replacing row 2 by row 1 minus row 2) does not change the determinant. For all nxn matrices A and B, we...
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...
Let A be an 3 x 3 matrix with the characteristic equation det(113 - A) = 13+ 12 – 22. Which of the following is not an eigenvalue of A? Select one: O a. 2 O b. 0 O c. 1 O d.-2
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....
(1 point) If det b 1 3 and det b 2 e 3 then a 5 det|b 5 el=15 and c 5 f c 8 f
(1 point) If det b 1 3 and det b 2 e 3 then a 5 det|b 5 el=15 and c 5 f c 8 f