MAT2114 HOMEWORK 06 2. (Your instructor forgot to do this example in class). Let W- (a) Find a matrix A so that W = Null(A). A-[117] = [1 CA (b) Find a basis for W. A: [ 1 1 1] > Bass (w). Singulur vector Pof R₂-R., 13-2, ER³ such that r+y+z=0 y = 0 Z Ax=0✓ 1x305x1 10

Q: The vector v with initial point (0, 0) is shown below. Write v in the form v=ai+bj, where a and b…

A: Given ,  The vector v with initial point (0, 0) We have to write v in the form v = a i + b j where…

Q: O Xply Hhe Cram- Schaidt to fraus fom the jven baris for R into an or themumal' tasis. Ue the veitos…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find a basis for Nul A and dim Nul A. 2 2 -1 -1 2 1 -2 0 1 A -1 1 0 0 -3 0 1 1] 1 -1

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Q: How are n, rank A, and nullity A related to each other how can one find a basis for Col A, Nul A,…

A: Write the relationship between n, rank A and nullity A. Also write a procedure to find a basis for…

Q: the set following value of the: 2 Which Furkant 19 a Furkan Ç ·R³? Mustafa F is a basis for Furkan C…

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Q: –30 . Let [x]B Let B = bi = ,b2 = be a basis for R2. Given x = be the coordinates of x relative to…

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Q: One of the following sets is a basis for R Select one: a. 2. O b. 1 2 C. 7. 3 S= 2 4 8 9. 9. 10 d.…

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Q: Let 4. -2 9. where c ER. What is the only value of c for which the set basis for R?

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Q: Determine whether each of the following sets is a basis for R. (a) S = 4 (b) S = 6. (c) S = 8 9. 5…

A: We have check determines whether the given sets are the basis for R3.

Q: Please provide explanation as to how the end result was obtained. Please be as explicit as possible.…

A: Use the matrix multiplication rule. According to this rule, the number of column of the 1st matrix…

Q: We showed in the text that z; - c; = 0 for a basic variable. Interpret sult. Y leaves the basis. it

A: Answer given below.

Q: The set S = is the standard basis for R?. The set A= {().()} The set A = is also a basis for R?…

A: VA=-2  1  -2  1=4  3-5+3.5-4  6  we expressed VA as linear combination of A basis vectors same VA…

Q: One of the following sets is a basis for R. Select one: a. 1 7 3 S=}| 2 10 O b. S= C. 1 2 S= d. 1 3…

A: A=111011001adj(A)=C11C21C31C12C22C32C13C23C33=1-1001-1001∴option C is  true

Q: 11. For what value(s) of k does the following set of vectors form a basis for R³? ·4·0 3 3

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Q: Question 31 Determine whether (V₁, V₂, V3} is a basis for R³. -3, V₂ = 8, V3 = 3 O Yes O No

A: Sol:- It will basis for R3 Only when , they will be linearly dependent i.e. determinant should be…

Q: 2. List all possible results and corresponding probability for measuring the state in the given…

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Q: Let [1 2 -5 11 -3 2 4 -5 15 2 A = 1 2 0 4 5 3 6 -5 19 -2 Find bases for Nul A and Col A.

A: According to the given information it is required to determine the bases for Nul A and Col A.

Q: 9. Given B = { (3,0,-3), (3,-2,1), (-1, -6,1)} and B' = {(1,1,–1),(0,1,2),(-1,1,0)}, find the…

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Q: The set S = { (0.6, 0.8, 0) , (0, 0, 1) , (-0.8, 0.6, 0) } is: Select one: O a. Basis for R4 O b.…

A: The solution is given as

Q: Determine whether S = {1-1,2t +31², 1²-21³,2+1³} is a basis for P3.

A: DEFINITION OF A BASIS-: A SET OF VECTORS v1,v2,v3,.......vn IS SAAD TO BE BASIS FOR A VECTOR SPACE V…

Q: Is S= { 2 3 2 3 1 1 a basis for M2.2 1 0 4 0 1 1 0 1

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Q: Let 1 2 3 -1 5 4 %3D 4 6 10 Which one is a basis for the null space, N(A"). of A a) {0} {E} b) O 1…

A: Given: Matrix A such that  To Find: Basis for null space of AT

Q: Let 1 2 3 -1 5 4 9. %3D 2 4610 Which one is a basis for the null space, N(A"). of A" a) O {0} b) O…

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Q: Let P2 denote the vector space of all polynomials in the variable a of degree less than or equal to…

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Q: 0555 if A = 0 0 0 0 then the basis fqf 0 205 N(A") is 1 .a Hạmmad Selawe .b كواے 1 .c 0.

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A: Let S=0101,1101 As the dimension of M22 is 4. Also, it has 4 elements, and so it is linearly…

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Q: DETER MINE WHETH ER TiHE SET Å IS A BASIS FOr IR9 2 %3D -2 EXPLAIN YOUR AN SWER MN- -m.

A: The given set S is not a basis for R^4.

Q: = 6 | [1 0 , E12 Eu = 8 En = 8 . and En = 7. Let E11 and E22 Use the {E11, E12, E21, E22} is a basis…

A: That's easy. Have a great day!!!