$. Let [1 5 -1 A = 2 11 3 16 Find a basis and the dimension for the row space of A and the column space of A.

Q: Find a basis for Col A and a basis for Nul A. - 3 9 - 2 - 7 A = 2 - 6 4 8 3 -9 -2 2 Also show that…

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Q: Let S = {1+ 5x, 1 – 2x-}. Which of the following polynomials could be added to the set S to form a…

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Q: Find a basis for the null space of the matrix. [10-7-4] 6) A = 01 5-2 [00 0 o] D) 明“

A: We have to find the basis for the null space of the matrix A.         According to our guidelines we…

Q: I 4 1 2 %3D O l 21I 1 2 0 2 2 16 1I -

A: By using row operation, we calculate the required basis and dimension.

Q: Do the polynomials x2 + 1, x? – 1, 2x – 1 form a basis in P2

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Q: [1 1 Let A = 0 1 li o -2. 3 Find the rank and a basis for the column space of A.

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Q: Suppose aj, az, az, a, and a, are vectors in R, and they are, in order from left to right, the five…

A: According to our guideline we can only answer first three subparts.

Q: The set B = {2 – 4x?, 8+ 3x – 16x2, 21 + 9x – 40x²} is a basis for P2. Find the coordinates of p(x)…

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Q: Determine whether the set {x2 + 2x - 3, 2x2 + x - 1, 3x2 + 2x - 2} is a basis for P, by solving the…

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Q: 2. Find the basis for the nullspace of A, and the nullity and rank of A

A: This is a problem of linear transformation.

Q: Find a basis for the set of all vectors in the form a + 2b + 3c 2а + 3b + 4с За + 4b + 5с [4а + 5b +…

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Q: (d) A basis of C(M) the column space of M (e) A basis of R(M) the row space of M

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Q: Find all values of a for which {[a? 0 1]. [0 a 2].[1 0 1]} is a basis for R3.

A: let v1=a2 0 1 , v2=0 a 2 and v3=1 0 1 be the three vectors in R3. now these vectors forms a basis of…

Q: Determine whether S is a basis for Pa. S = (3- 4t2 + t,-3 + t2, 2t + te, 6t) O S is a basis of P3. O…

A: Given that      S = {3-4t2+t3 , -3+t2 , 2t+t3 , 6t}

Q: Find a basis for the column space of B and a basis for the null space of B, -2 -1 1 1 -8 3 2 -4 -2…

A: Null Space: Null space of matrix A is given by N(A)=x∈V  Ax=0  where V is a vector space.Column…

Q: 5. Consider the space {) a a + b+c= d : 2a + b = d a + b+ 3c = 0 H = CRª. C d (a) Find a matrix A…

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Q: Add one vector to the set S = so that S is a basis for R

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Q: b) Find the value of k such that (-1,1,1), (1,1,1), (1, -1, k) form a basis of R²

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Q: (d) Find a basis for the column space of A. .........

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Q: Find [Q(v2, i) : Q] and a basis for Q(V2, i) over Q. [Hints: Use the degree and a basis for V2) over…

A: Given: To find ℚ(2, i): ℚ  and basis for ℚ(2, i) over ℚ.

Q: ind a basis for the column space of -1 -1 0 -4 2 A = 3 -3 -2 -2 0 6 Sasis =

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Q: (c) Find a basis for the row space of A.

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Q: Let B = {x²+x,-2x² + 3x + 3, 2x² – x – 2} be a basis of P2(R)

A: Given,            B=x2+x,  -2x2+3x+3,  2x2-x-2

Q: 7

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Q: The set 1 [O 01 B : is a basis of the space of upper-triangular 2 x 2 matrices. -3 -27 Find the…

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Q: Г1 2 0 1 2 4 1 - A = 3 6 -1 8 4 8 -1 12 8

A: Given matrix is A=1203124−15436−18548−1128. We have to find a basis for the null space of the matrix…

Q: Consider a basis for a space given by vectors -5 0 -10 -4 2 -5 -10 0 -10 -2 6 0 Answer the following…

A: answer is in next step. please give a like!!!!

Q: -4 1 3 A = 3 -4 2 3 4 -1 -3 A basis for the column space of A is { }

A: The given matrix is:…

Q: 2. let A = 2 4 and W= d. Find a basis for NulA. e. Find a basis for RowA.

A: Given that, A=11102410-1 (a) The null space of A is of the form, X=x1x2x3 such that, AX=0. That is X…

Q: If Col A has dimension 3, then the first three nonzero columns of A form a basis for Col A. True…

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Q: Find a basis for the column space of 2 4 A = -2 -3 1 2 -3 3.

A: A=-1204-1-23-312-33 Now, reduce the matrix to row echelon form  =-12040-43-704-37R2→R2-R1R3→R3+R1…

Q: Find the basis of the null space and basis of the column space.

A: Consider the provided matrix A, First reduce the matrix A into the row echelon form,

Q: Let B = {1+x, 1– 3x?, x + 6x²} and p(x) = 12 + 8x + 9x?. You are given that B is a basis for P2. If…

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Q: Find a basis for R³ including as many columns of A as possible.

A: First we will find the column space of A and then we will extend the column space of A into the…

Q: 1001 0 110 1-1 Find a basis of the row space of A= by reducing A to reduced echelon form. 1012 2…

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Q: 1 2 1 0 2 5 1 1 Given A = 3 7 2 2 L4 9 3 -1 Which of the following is not a basis for column space…

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Q: 9 - - Let 1 3 5 A = -1 5 4 9 2 4 6 10 Which one is a basis for the column space, C(A), of A

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Q: -2 0 1] 2 1? 1 Which of the following is a basis for the column space of -1 -4 2 4 27 2 | 2 1 -1 2 2…

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Q: 1 0 4 0 5 5 5 2 1 3 3 3 Let A = Find basis for the column space of A

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Q: Let 1 -1 1 1 2 A : y = 1 x = 1 -2 4 1 1 -1 -2 (a) Is x in the column space of A? (b) Is y is the…

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Q: 1 3 2 5 Find a basis for the Null Space and a basis for the Column Space of A 1 3 2 6

A: We have given a matrix 13251326 Now we wanna to reduce our matrix in row echelon form  for this C1 →…

Q: .. Find A basis for the nullspace and column space of 1 2 1 1 2 2 2 4 3 2 1 1 2 A = 3 3 1 -1 -1 |

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Q: 1 ! 4 | 2 %3D ol 2 1 I 1 2 1 -| 0 0 2 2 16 1

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Q: Determine whether S is a basis for P3. S = {6 – 2t2 + t³, -4 + t2, 3t + t³, 5t} O sis a basis of P3.…

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Q: The vectors 02 = 6. 03 = form a basis for R' if and only if k +

A: Given vectors are: v1→=4-10,v2→=-666,v3→=24k We have to find the value of k when the vectors form…

Q: [1 2 1 0 2 5 1 1 3 7 2 2 L4 9 3 -1 Given A = Which of the following is not a basis for row space of…

A: Reduce the matrix to echelon form. Apply the elementary row operations.  Apply R2→R2-2R1.…

Q: Given the set S = {M1, M2, M3, M4}, where 3 1 2 M1 = M2 2 4 1 -3 0 -2 1 1 M3 M4 4 1 2 -1 (a) Show…

A: We will find out the required solution.

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.