Math 2890 QZ-6 SP 2018 1) Find the rank of the following matrix. Also find a basis for the row and column spaces. 1 0 3 3 10 0 -1 2 Find a basis of Null(A) where A is the given matrix. Find the rank of A and dimension of Nul(A). Let B be an invertible 4X4 matrix (a matrix with 4 rows and 4 columns). Is the matrix AATB also invertible? Explain.
QUESTION 4 (-2 1 -4 2 -1 6 Find the rank and nullity of the matrix A. A= 1 2 -1 10 ) A Rank(A)=1 and Nullity(A)=2. OB. Rank(A)=2 and Nullity(A)=1. oc Rank(A)=3 and Nullity(A)=0. OD. Rank(A) = 0 and Nullity(A)=3.
Q 11 - Rank the following in the order of their increasing acidity (least to most) COOH COOH COOH HOOC COOH a. 4<1<3< 2 b. 4<2<3<1 c. 2<3<1<4 d. 1<3<2<4 e. none of these Q 12 - Rank the following in the order of their increasing reactivity to nucleophiles (least to most) INH 4 a. 4<1<3<2. b. 3<2<4<1 c. 2<3<1<4 d. 1<3<2<4 e. 3<2<1<4 Q 13 - Draw the skeletal structure of the following molecules. A) Trifluoroacetic anhydride B) Benzyl...
Find a basis for the row space and the rank of the matrix. -3 -6 6 5 4 -4 -4 2 -3 -6 6 9 (a) a basis for the row space 33} (b) the rank of the matrix 3
10 p. 2 Calculate the rank of the following matrix A 1 2 1-1 3 6 -3 -1 -2 1 2 27 1 1 4 4
linear alebra can you do problems 5&6 please. 5. If A is 2 by 3 and B is 3 by 2 ani AB = 1, show from its rank that BA 1. 3 points 6. Find the LU factorization of the matrix for the matrix A [10 points A=11-1 0 1-14 0 -4 What is the LDU factorization? Find the complete solution of Ar = b with b given above. 5. If A is 2 by 3 and B is...
(6) Let A denote an m x n matrix. Prove that rank A < 1 if and only if A = BC. Where B is an m x 1 matrix and C is a 1 xn matrix. Solution (7) Do the following: (a) Use proof by induction to find a formula for for all positive integers n and for alld E R. Solution ... 2 for all positive (b) Find a closed formula for each entry of A" where A...
three small problem!!!!! Problem 7: (9 total points) Let A 11 0 -1 2 1 -1 3 -1 0 = 1 | -2 1 4 -13 3 -1 -5 1 -6 a) Find a basis for ker A. b) Find a 5 x 5 matrix M with rank 2 such that AM = 0, where is the 4 x 5 zero matrix. is the 4 x 5 zero matrix. Prove c) Suppose that B is a 5 x 5 matrix...
linear algebra Recall the Rank Theorem, which states that if A is an mxn matrix, then rank(A) + nullity(A) = n. Recall the given matrix A. A = [ 3 -6 0 3 11 -1 2 1 3 6 [ 2 -4 1 6 7 This is a 3 x matrix, so n = . Furthermore, we previously determined that rank(A) - 2. Substitute these values into the formula from the Rank Theorem and solve for nullity(A). rank(A) + nullity(A)...
(1 point) Find the value of k for which the matrix -8 2 4 A= - 71 -5 -3 3 k has rank 2. k =