Please do both question. Thank you!!!
Please do both question. Thank you!!! Let -3 -3 -1 A= 4 -1 -3 | 0...
Question 1. La 1 2] Let A = 6 3 4 Lc 5 6 for some a, b, c ER such that det A = 12. (a) (9 points) Determine the dimension of the column space of A. (Th mine the rank of A.) Justify your answer. (h) (8 points) Calculate the determinant of La-1 1 2] 6 - 2 3 4 - 3 5 6 (c) (8 points) Calculate the determinant of La 3 37 6 7 6 |...
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-...
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 13 For what values of a does the system below have nontrivial solutions? 3x+3y-2z=0 -6x+ay+4z=0 2x+4y +4z=0 a) -4 b) 06 c) -2 d) 2 e) 3 f) None of the above. Review Later
need help with e f and g please 2x2 + x3 0 (1 pts) write the linear system in the format, A x = b (2 pts) Find the determinant of the matrix A by using an expansion along row 1 (2 pts) Find the determinant of the matrix A by using an expansion along column 2 Compare the result with that of (b). Based on your result of b and/or c is matrix A singular or invertible (2 pts)...
Determine which property of determinants the equation illustrates. 1 3 2 0 0 0 96 -8 = 0 If one row of a matrix is a multiple of another row, then the determinant of the matrix is zero. If one row of a matrix consists entirely of zeros, then the determinant of the matrix is zero. If two columns of a matrix are interchanged, then the determinant of the matrix changes sign. If a row of a matrix is multiplied...
[1 -1 0 0 -2 0] 1 4 -4 0 0 -8 0 (1 point) Let A = 10 0 -1 2 -3 3 . Find a basis for the row space of A, a basis for the column space of A, a basis for the null space 0 0 0 -3 0 -2 Lo 0 1 0 3 3] [1 -1 0 0 -2 01 0 0 1 0 3 0 of A, the rank of A, and the...
4. Express the Boolean functions F as both a sum-of-minterms and a product-of-maxterms 1 0 0 0 Express the following function as a sum-of-minterms F(a, y,z) (zy)' +zy+ Convert the function from the above question into a prodtuct-of macterms Use the K-map to simplify the three variable Boolean functions F(u,x, y, z) = Σ (0, 2, 3, 4, 5, 8, 12, 15) 00 01 11 10 00 10 11 01 1 1 0 0 11 1 0 0 0 10...
Question 17 (2 points) Let A be a 3 x 4 matrix with a column space of dimension 2. What is the dimension of the row space of A? Not enough information has been given. O 1/2 3 2. Question 16 (2 points) The rank of the matrix 1 2 - 1 2 4 2 1 2 3 is 02 O none of the given options Question 15 (2 points) Which of the following is not a vector space because...
Question 11 Given: f" (z) = (4x +9)88(3:+1)*(5x - 1)(x - 2)", where Dom f (z) = (-00,0). Fird- Doint(s) of f(x). - - *(-)). (-5,+(-)), (6,+(?)), and (2,5 (2) (54(++)), ($,f(t)), and (2,5 (2) (5.1()) and (2,5 (2) - none