Homework Answers
Add Answer to:
3. Consider the following vectors, where k is some real number. H-11 Lol 1-1 a. For what values of k are the vectors linearly independent? b. For what values of k are the vectors linearly depende...
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1...
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29...
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearl...
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
0 6. 11 points HoltLinAlg2 10.2.012. My Notes Ask Your Teacher Find projsf for Rx)- ex, where S-span1, x and the inner product is eBook 7. 1 points HoltLinAlg2 10.2.014 My Notes Ask Your Teacher Use...
0 6. 11 points HoltLinAlg2 10.2.012. My Notes Ask Your Teacher Find projsf for Rx)- ex, where S-span1, x and the inner product is eBook 7. 1 points HoltLinAlg2 10.2.014 My Notes Ask Your Teacher Use the Gram-Schmidt process to convert the given set of vectors to an orthogonal basis with respect to the given inner product. (Apply the Gram-Schmidt process in the order the vectors are given and do not normalize.) The set,1,0with respect to the inner product (u,...
When dealing with standard vectors (with purely real elements) we are used to finding the angle...
When dealing with standard vectors (with purely real elements) we are used to finding the angle between the vector from But what happens when we are dealing with vectors that have complex elements. In quantum mechanics, in general, the inner product is a complex number, which does not define a real angle The Schwarz Inequality helps us in this regard However, according to it, the only thing we can know is that the absolute value of the inner product is...
Question 1 (10 points) Projection matrix and Normal equation: Consider the vectors v1 = (1, 2,...
Question 1 (10 points) Projection matrix and Normal equation: Consider the vectors v1 = (1, 2, 1), V2 = (2,4, 2), V3 = (0,1,0), and v4 = (3, 7,3). (a) (2 points) Obtain a basis for R3 that includes as many of these vectors as possible. (b) (4 points) Obtain the orthogonal projection matrices onto the plane V = span{v1, v3} and its perpendicular complement V+. (c) (2 points) Use this result to decompose the vector b= (-1,1,1) into a...
1. Consider the following three vectors in R Vi (1,-1,-11), v2 (3,0,-3,2), v3- (4,0,-2,2) (a) Perform...
1. Consider the following three vectors in R Vi (1,-1,-11), v2 (3,0,-3,2), v3- (4,0,-2,2) (a) Perform the Gram-Schmidt process to find an orthonormal basis [ei,e2,e3j of the subspace spanned by {vi, V2, V3) (b) Find the QR decomposition of the following matrix A QR: 412 922 231 12 113 q13 q23 43300 14 924 934 -1 0 0 0 122 r23 Relate (rij] to the Gram-Schmidt process. (c) Can you say anything about either Qor without calculation? Show that ATA...
please answer the following question with detailed step 1 1. Consider vi = 2 V2 =...
please answer the following question with detailed step
1 1. Consider vi = 2 V2 = a and v3 = -1 (a) Find the value(s) of a such that 01,02 and v3 are linearly dependent and write Vi as a linear combination of v2 and 03, if possible. (b) Suppose a = 0, write v = 2 as a linear combination of v1, V2 and 03. (c) Suppose a = 0, use the Gram-Schmidt process to transform {V1, V2, V3}...
2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α 0 and for every 0 < i k one has that α, κ α, > , αϊ-1 3. Find a l...
2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α 0 and for every 0 < i k one has that α, κ α, > , αϊ-1 3. Find a linear system with real coefficients for which the span of
2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α...
the last pic is number 14 please answer it as a,b,c,d as well. thanks 1. If...
the last pic is number 14 please answer it as a,b,c,d as
well.
thanks
1. If A is diagonalizable then A is diagonalizable. a) True b) The statement is incomplete c) False d) None of the above 2. In every vector space the vector (-1)u is equal to? a) -U b) All of the above c) None of the above d) u 3. The set of vectors {} is linearly dependent for a) k = 3 b) k = 1...
#8. Let W be the subspace of R3 spanned by the two linearly independent vectors v1 = (-1,2,2) and v2 = (3, -3,0). (a) Use the Gram-Schmidt orthogonalization process to find an orthonormal basis for W. (b) Use part (a) to find the matrix M of the orthogonal projection P: R W . (c) Given that im(P) = W, what is rank(M)?
1 -1.2 5 Uį = U2 = -3 1, U3 = 2 , 14 = 29 ( 7 Answer the following questions and give proper explanations. (a) Is {ui, U2, uz} a basis for R3? (b) Is {ui, U2, u4} a basis for R4? (c) Is {ui, U2, U3, U4, u; } a basis for R? (d) Is {ui, U2, U3, u} a basis for Rº?! (e) Are ui, u, and O linearly independent?! Problem 6. (15 points). Let A...
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
0 6. 11 points HoltLinAlg2 10.2.012. My Notes Ask Your Teacher Find projsf for Rx)- ex, where S-span1, x and the inner product is eBook 7. 1 points HoltLinAlg2 10.2.014 My Notes Ask Your Teacher Use the Gram-Schmidt process to convert the given set of vectors to an orthogonal basis with respect to the given inner product. (Apply the Gram-Schmidt process in the order the vectors are given and do not normalize.) The set,1,0with respect to the inner product (u,...
When dealing with standard vectors (with purely real elements) we are used to finding the angle between the vector from But what happens when we are dealing with vectors that have complex elements. In quantum mechanics, in general, the inner product is a complex number, which does not define a real angle The Schwarz Inequality helps us in this regard However, according to it, the only thing we can know is that the absolute value of the inner product is...
Question 1 (10 points) Projection matrix and Normal equation: Consider the vectors v1 = (1, 2, 1), V2 = (2,4, 2), V3 = (0,1,0), and v4 = (3, 7,3). (a) (2 points) Obtain a basis for R3 that includes as many of these vectors as possible. (b) (4 points) Obtain the orthogonal projection matrices onto the plane V = span{v1, v3} and its perpendicular complement V+. (c) (2 points) Use this result to decompose the vector b= (-1,1,1) into a...
1. Consider the following three vectors in R Vi (1,-1,-11), v2 (3,0,-3,2), v3- (4,0,-2,2) (a) Perform the Gram-Schmidt process to find an orthonormal basis [ei,e2,e3j of the subspace spanned by {vi, V2, V3) (b) Find the QR decomposition of the following matrix A QR: 412 922 231 12 113 q13 q23 43300 14 924 934 -1 0 0 0 122 r23 Relate (rij] to the Gram-Schmidt process. (c) Can you say anything about either Qor without calculation? Show that ATA...
please answer the following question with detailed step
1 1. Consider vi = 2 V2 = a and v3 = -1 (a) Find the value(s) of a such that 01,02 and v3 are linearly dependent and write Vi as a linear combination of v2 and 03, if possible. (b) Suppose a = 0, write v = 2 as a linear combination of v1, V2 and 03. (c) Suppose a = 0, use the Gram-Schmidt process to transform {V1, V2, V3}...
2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α 0 and for every 0 < i k one has that α, κ α, > , αϊ-1 3. Find a linear system with real coefficients for which the span of
2. a. Define that the vectors α, α 2, ,Ak are linearly independent. b. Prove that α, α 2, ,Ak are linearly independent if α...
the last pic is number 14 please answer it as a,b,c,d as
well.
thanks
1. If A is diagonalizable then A is diagonalizable. a) True b) The statement is incomplete c) False d) None of the above 2. In every vector space the vector (-1)u is equal to? a) -U b) All of the above c) None of the above d) u 3. The set of vectors {} is linearly dependent for a) k = 3 b) k = 1...
Most questions answered within 3 hours.
-
(63
#14)
which of the following statments best describes how chamging
the concentration of the substances...
asked 1 hour ago -
In the following reaction, which element is undergoing
oxidation: Na2SO3 + N2O --> N2 + Na2SO4...
asked 1 hour ago -
Which of the following pairs of ions have the same electron
configuration?
I: Br− and Se2−...
asked 4 hours ago -
The Foremost Composite Materials Company is planning a two-day
sales conference for October 19-20. The conference...
asked 4 hours ago -
3) Illustrate the observed pattern of relatedness of organisms
versus adaptations to specific conditions. This means...
asked 5 hours ago -
In winter a lake has a 0.35 m thick ice layer over 1.10 m of
water....
asked 6 hours ago -
Assuming the following has been encrypted with a Vigenere cipher
below, use the method(s) and assumptions...
asked 6 hours ago -
How would I use switch statements to write a program that will
take an input of...
asked 6 hours ago -
Imagine a reaction in which methane gas combusts at a constant
pressure of 1 atm and...
asked 6 hours ago -
Two parallel wires (each 12 m in length) are separated by a
distance of 0.065 m...
asked 6 hours ago -
Suppose there were three masses at the corner of uniform
equilateral triangle. The masses are m1...
asked 6 hours ago -
Situation: A building that is 618 m above the ground floor. How
many times would a...
asked 6 hours ago