ſi 3 5] 1) (5 points) Compute the determinant of A= | 2 -2 1 using...
ſi 0 1 37 14 00 11 1. Compute the determinant of 10 4 11 5 using cofactors. Show your work. 12 0 1 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-...
4. (3 points) Let ſi 2 1] A= 0 4 3 [1 2 2 Compute the third column of A-1 by solving the equation Ax = es, where ez = 0 Hint: Use Cramar's rule to solve the equation, noticing that the third column of A-' is given by the solution of the above equation. In fact there is nothing special about A-1, the third column of any 3 x 3 matrix B is given by the product Bez. Can...
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...
2. [16 marks) - T (a) Evaluate the determinant of matrix A where: ſi 3 -1 0 2 -4 A= -2 -6 2 3 37 - 38 (b) Solve the following system of equations for 23 only, by using Cramer's Rule: [Again, your answer to part(a) may be helpful!] 21 +3.02 – 23 2x2 - 4.23 - 24 -221 - 602 +213 +324 3.01 + 7.02 – 3x3 +8.04 = 1 = 0 = -2 = 0 (c) Use your...
Linear Algebra question.
Problem 7. Find the following determinant by the method of elimination, i.e., by using row operations and keeping track of the effect of the row operations on the determinant. Show the row operations one by one stating which row operation you are using, and show the effect on the determinant formula. You can use a calculator to perform the row operations if you wish. Sorry, no credit for finding it by another method. 4 5 2 1...
[10] 3. By using only row echelon operations compute the determinant of the matrix 10 25 - 15 A=| 1 2 4 8 12-16
Compute the determinant of the following matrix using a cofactor expansion across the first row. 6 2 - 2 A= 50 35 4 0 N Compute the determinant using a cofactor expansion across the first row. Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer.) OA. Using this expansion, the determinant is (6)(-30) - (2)(2)+(-2)(25)= OB. Using this expansion, the determinant is (6)(-30)+(5)(2)+(3)(25) = OC. Using this expansion, the determinant is...
2. Compute the determinant of the following matrices. (a) 2 -1 2 5 -4 A= 3 -11 9 0 (b) 1 2 1 2 1 A= -1 -1 2 1 1 2 (apply row reductions combined with cofactor expansion)
6. Find the determinant of the following matrix using elementary row operations. (Turn the elements above the main diagonal into zeros to have the least amount of calculations.) (10 points) -1 -9 0 -2 -4 -2 -2 4 3 -1 -1 4 3 2 1