

Question 1 Let A 6 b- > [|1 and C 5 -2 3. Calculate the following:...
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-
8 Let t and s be real numbers and let C = [cij]. Prove (s +t)C = sC+tC. ution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will submit your work as ar
12 points Let L: R3 → R3 defined by L U2 (1 3 57 rui 1 2||uz. Find ker L and dim ker L. LO 2 3] [u be your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will submit your work as one PDF file after it the test.
2) Let V = R2 and let u = 11 points Save Answer and v= Cl be vectors in R2. Define (u, v) = 2uv - 4 U2 - uzv. + 6u2V2. a) Find (u, v) where u = Lola and v= = [1 b) Determine the length of v in the inner produce space. c) Determine real number a such that u and v are orthogonal. Do not type your solution (work and answer) in the textbox below. Only...
Part C Only
Let Σ = {a,b}. For each of the following languages, find a grammar that generates it. (a) Li {a"6" : n > 0,m< n}. (b) L2 = {ang 2n: n > 2). (c) L3 {an+35" : n > 2}.
xt yt z=2 Solve the system using Gaussian Elimination or Gauss-Jordan reduction. 6x - 4y + 5z = 31 5x + 2y + 2z = 13 3 points Do not type your solution (work and answer) in the textbox below. Only work on your blank sheets of paper. You will submit your work as one PDF file after you submit the test. Τ Τ Τ Τ Paragraph Arial 3 (12pt) ET TT, S % DOQ CHE n 4 Question 4...
Let descrete random variable X ~ Bin(9,0.4) Find: 1) Probability P(X>4) 2) Probability P(X> 2) 3) Probability P(2 <X<5) 4) Probability P(2<X<5) 5) Probability P(X =0) 6) Probability P(X =6) 7) ux 8) OX Show your explanations. Displaying only the final answer is not enough to get credit. Note: round calculated numerical values to the fourth decimal place where applicable.
-4 0 -1 1 1 2 7 6 (1 pt) Let A 1 5 -3 -1 3 13 -1 -1 Find orthogonal bases of the kernel and image of A 10 -1 1 2 Basis of the kernel: -1 1 -1 3 -3 1 8 Basis of the image: -1 1 -1 7 (1 pt) Perform the Gram-Schmidt process on the following sequence of vectors. -3 -2 6 -3 6 y= -5 х — 3 -4 3 1 2 -2...
linear algebra
3. Let A be the following matrix: A= 0 -2 6 0 0 C 6 C 02 0 0 8 0 0 5 T 3 -1 7 6 2 - 4 04 (a) Find det(A). Show your work Express your answer in terms of x. (b) Identify the value(s) of x for Nul (A) = {0}.
5 (10) A (5) (6) 18 4 (12) (9) 2 (0) B 4 18 E > H'S (7) С. C (8) 3 (4 ) Complete the following table using the search graph on the previous page only. The "path found" and "path cost" are the path output by the search algorithm and its cost. Consider a state as being “expanded” if it is the element of a node in the search tree that was expanded. List "states reached or expanded”...