linear algebra 1 0 0 0 1 1 0 0 1. Let A be the 4 x 4 matrix: A= 1 1 1 0 1 1 1 1 (a) Find A-1 by hand. (b) Let T be defined by T(T) = Aē. Use your answer to (a) to find all vectors T E R4 such that: T(T) = 2 4 -9 0 (c) Which of the following statements are true? (Select all that apply) A. The columns of A form...
3 3 -16 -2 -5 12 4 1-12 Find the reduced row echelon form of the matrix B 0 0 0 0 0 0 -16 12 -5 1, and v3 = 1-12 Let Vi 4 17 5 Decide whether the following statements are true or false. 2 The vectors vi, V2, and v span R. The vectors vi , V2 , and V3 are linearly independent. 3 3-16 В 1-2-5 4 -1 -12 Find the reduced row echelon form of...
2 5 Do the vectors u = and v= 3 7 span R3? -1 1 Explain! Hint: Use Let a, a2,ap be vectors in R", let A = [a1a2..ap The following statements are equivalent. 1. ai,a2,..,a, span R" = # of rows of A. 2. A has a pivot position in every row, that is, rank(A) Select one: Oa. No since rank([uv]) < 2 3=# of rows of the matrix [uv b.Yes since rank([uv]) =2 = # of columns of...
1 -3 1 4 - 21 2. Let A= 1 1 3 06 0 1 -1 5-5 2 Do the columns of A span Rº? What does this mean for the general matrix equation Ax = b where be R*? 5 3. (a) Determine if A = 7 homogeneous equation. (8pts) -3 -4 5 2 1 has at least one free variable by solving the 0
Consider the matrix 0 4 8 24 0-3-6 3 18 A-0 24 2 -12 0 -2-3 0 7 0 3 5 [51 [51 a) Find a basis for the row space Row(A) of A (b) Find a basis for the column space Col(A) of A (c) Find a basis space d) Find the rank Rank(A) and the nullity of A (e) Determine if the vector v (1,4,-2,5,2) belongs to the null space of A. - As always,[5 is for the...
Define the linear transformation T by T(x) -Ax 12-1 41 3 12-1 (a) Find the kernel of T. (If there are an infinite number of solutions use t as your parameter.) ker(T) (b) Find the range of T spant(1, 0, -1, 0), (0, 0, 0, 1)) span (1, 0, -1, o), (0, 1, -1, 0) spant(1, 0, -1, o), (0, 1, -1, 0), (0, 0, 0, 1)) R4 R3 O S
2 3 12 3 37 1. Let A - 10 15 40 7 1131 2 3 7 2 2 and B 1-2 -3 8 3 171 echelon form of A. (Assume this!) (a) (2 pt) What is the value of rank(A)? 110057 100 100 000121The B is the reduced to loooool (b) (2 pt) What is the value of nullity(AT)? (Read carefully (C) (3 pt) Find a basis for col(A). Circle your final answer. (d) (3 pt) Find a basis...
6201-16000-MATH-2318 Afeez Amusan & Time Remaining: Quiz: Quiz 2 (1.3, 1.4), Part 1 This Question: 7 pts 11 of 17 (7 complete) This Vocan each vector in R* be written as a linear combination of the columns of the matrix A? Do the columns of A span R7 24 -7 16 - 1 - 1 1 - 3 0 -6 15 -30 ² 0 3 6 1 1 Can each vector in R4 be written as a linear combination of...
1 2 -1 0 0 1 0 0 -1 3 ſi 2 0 2 5 [10 (11 points) The matrix A= 2 1 3 2 7 reduces to R= 0 3 1 a 6 5 0 1 Let ui, , 13, 144, and us be the columns of U. (a) Determine, with justification, whether each of the following sets is linearly independent or linearly dependent. i. {u1, 12, 13) ii. {u1, 13, us} iii. {u2, 13} iv. {u1, 12, 13,...
Determine if the columns of the matrix form a linearly independent set. 1 2 - 3 8 12 37 -6 38 - 1 -8 Select the correct choice below and fill in the answer box to complete your choice. A. The columns are not linearly independent because the reduced row echelon form of [ A o]is | The columns are linearly independent because the reduced row echelon form of [ A 0 ] is B.