could someone explain this and give me a problem example
could someone explain this and give me a problem example • Compute the determinant of a...
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....
6. (5 points) Suppose the elementary matrix E is of this form (a) Compute the matrix multiplication EB (b) Compute the determinant of EB using the cofactor expansion along the 1st row of the matrix, and show that the determinant is equal to -det(B) (MUST use the cofactor expansion, no points will be given for other meth- ods.) Hint: Same, don't expand everything out, you will be drown in a sea of bij, you should look at the cofactor expansion...
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...
Determine whether A is diagonalizable. 2 0 2 A = 0 2 2 2 2 0 Yes No Find an invertible matrix P and a diagonal matrix D such that p-1AP = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list. If A is not diagonalizable, enter NO SOLUTION.) (D, P) = Compute the determinant using cofactor expansion along the first row and along the first column. -1 1 -1...
(12 points) Evaluate the determinant of the matrix D using cofactor expansion down the second column, then find det(3D) and det((2D)-1). D = [ 1 -5 301 3 0 4 3 -1 0 -3 0 I 3 8 6 2
3. Let A 2 -30 1 0 -2 2 0 (i) Compute the determinant of A using the cofactor expansion technique along (a) row 1 and (b) column 3. (ii) In trying to find the inverse of A, applying four elementary row operations reduces the aug- mented matrix [A1] to -2 0 0 0 0 -2 2 1 3 0 1 0 1 0 -2 Continue with row reductions to obtain the augmented matrix [1|A-') and thus give the in-...
Compute the determinant by cofactor expansion. At each step, choose a row or column that involves the least amount of computation. 5 0 0 5 4 8 3 - 7 (Simplify your answer.) O 3 0 0 9 2 1 7
Compute the determinant by cofactor expansion. At each step, choose a row or column that involves the least amount of computation. 100 5 3 7 3 - 8 200 0 5 3 1 4 1 0 0 3 7 3 200 8 (Simplify your answer.) 5 3 1 4
Compute the determinant by cofactor expansion. At each step, choose a row or column that involves the least amount of computation 300 5 4 7 3 - 4 200 0 6 3 1 7 5 300 4 7 3 -4 = (Simplify your answer.) 200 0 6 3 1 7
Compute the determinant by cofactor expansion. At each step, choose a row or column that involves the least amount of computation. 5 2 2 40 3 0-4 1 0 4 - 8 34 1 3 0 0 0 0 9 3 4 30 5 2 24 0 3 0-4 1 0 4 - 8 3 4 1 = 3 0 000 9 3 4 30 (Simplify your answer.)