Let 0 1 -1 0 1 A = -2 1 0 1 -1 1 0 2 -1 2 -1 Find a basis for the nullspace of A.

Q: 1. Determine whether the following vectors form a basis for R. -2 11

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Q: Find a basis for the nullspace of A. 6. 1 - 1 A=5 - 4 -4 7 -6 (a) 3 2

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Q: Let 10 1-1 0 A = -2 1 0 1 -1 0 1 02-1 -1 Find a basis for the nullspace of A.

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Q: Determine if (f1, f2, f3, f4, f8) is a basis of R4[x].

A: Given:    f1=1+x+x2+x4f2=x+x2+x3+x4f3=x+2x2+x4f4=1+3x+4x2+2x3f8=1-x2 Check {f1, f2, f3, f4, f8} is a…

Q: Let 9. A = 3 9 4 6. -3 2 -2 Find an orthonormal basis of the kernel of A.

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Q: Let -4 -6 4 6. A = 6. 2 -2 -6 Find an orthonormal basis of the kernel of A.

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Q: Explain why S is not a basis for P2. S = {1 - x, 1 – x², -1 – 3x + 4x²} O is linearly dependent. O s…

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Q: Let B = be basis for R. Find the dual basis B* of B

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Q: Let A = 3.6 1 -8 Find an orthonormal basis of the image of A.

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Q: Let, a1, a2 and a3 are the basis for R. [R1] y = |R2 [R3] a1 = |0 a2 = |0 a3 = Find the following:…

A: Since you've asked multiple questions, as per our answering guidelines we are supposed to solve the…

Q: Find a basis for the null space of A -3 6 -1 1 -7 A = 1 -2 2 -1 2 -4 5 8 -4 3.

A: Given    A=-36-11-71-223-12-458-4We first find reduced row echelon form of  A.      Applying…

Q: Find a basis for the null space of A -3 -1 1 -7 A = 1 -2 2 3 -1 -4 5 8. -4

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Q: 1: Find a basis and determine the dimension of the following sub-spaces. H = { : 1a-c=0}. a b {:…

A: We have to find the basis and dimension of subspace

Q: Give a basis for the null space of the matrix A. 100-4 A =0 10 3 %3D 0 01 2

A: Given a matrix  A = 100-401030012 As this matrix is already in row reduced echelon form , then the…

Q: . If {x1, X2, X3} is a basis of V3 (R), show that {x, +x2, X2 + x3, X3 + X1} _is also a basis of V3…

A: Given problem is :

Q: Determine if S is a basis of P3. S = {1-t, 2t + 3t2, t2 - 2t3, 2+t3}

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Q: Let S = {x; 2 – x; x² – 2x}. A. S is a basis of P2 B. S is a basis of P C. None of the above

A: Let S=x, 2-x, x2-2xSince, we know that If V is a vector space of dimension n  (say) and…

Q: Find the basis of the null space of A. 3 1 1 2 A = 4 1 2 1 1 –1 1 1 1 -1 [2 2 1 2 1 2

A: Step 1: Transform the matrix to the reduced row echelon form

Q: Let p1,P2, P3 € P2 be defined by p1(t) = 2+t+t2, p2(t) = 2 – t+ 3t2, and p3(t) = 10+t+9t². Determine…

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Q: 1 0 1 Find a basis for the null space of the matrix A = 0 0 0 9 0 9

A: Basis of null space is the solution of AX=0.

Q: Say whether the polynomials P1 (x) = x³–7x²+4x, p2(x) = 3x³-x²+5x-1, p3(x) = x³+4x-x²+1 are linearly…

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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 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: 6. Determine the basis for the null space of -2x + 2y + 2z] a) 3x + 5y + z 2y + z х — 2у — z b) -x +…

A: Introduction: Null Space, like Row and Column Space, is a simple area in a matrix, including all…

Q: Find a basis for the null space of matrix A. 1 0 A = 0 1 0 0 0 -3 2 -1] %3D -5 3 A basis is -3 1

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Q: Let 1 5 A 3 3 -6 2 0 5 Find an orthonormal basis of the column space of A.

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Q: Find a basis for the null space of the matrix: [1 A = -1 -1 1 4

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Q: Let -4 4 -4 -4 Find a basis for the null space of A. {

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Q: Let 6 9. A = -6 -9 A basis for the null space of A is

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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 -2 -1 -2 -6 -1 2 -2 A 1 -3 -7 -1 2 3 4 7 Find orthonormal bases of the kernel and image of A.…

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Q: Let [2 A = 3 4 2 1 -9 2 -6 nd an orthonormal basis of the kernel of A.

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Q: Let O 0 10 -1 A = |0 0 0 1 3 1 4 0 0 A basis for Null(A) is given by:

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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: Let 1 -6 -2 A 1 -3 1 3 -8 4 Find an orthonormal basis of the column space of A.

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Q: - 3x3 + 7x4 = 0 X1 -7x2 - 4x4 = 0

A: The solution are next step is..

Q: 0 1 5 -1 0 0 -2 1 13 0 1 5 -1 0 0 for the column space of A. (If a basis doe

A: Introduction: It is given that the matrix A is, A=10-4-3-21135015-1~10-4-3015-10000. We have to find…

Q: Let S= {2x- x²,1+x+x²,2+5x} and p= -1-2x+3x². The set S is a basis for P2. (p)s= (a,b,c) with a = b=…

A: Given S = {2x-x2, 1+x+x2, 2+5x}  and P = -1-2x+3x2  The set S is a Basis for P2   Let the vectors…

Q: [1 1 -2 1] 0 0 -1 1 0 0 0 0 Find a basis for the nullspace of B

A: B=11-2100-110000

Q: 1 0 1 1 -1 0 0 A =| -2 1 1 -1 1 0 2 -1 2 -1 Find a basis for the nullspace of A.

A: Let B be a matrix of the dimension, m×n .Then, the null space of B is the set of solutions to the…

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 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: Show that the polynomials P1 = 1+x + x² P2 = x + x² P3 = x2 form a basis for P2.

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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: .. 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: 60. In R4, given a nullspace V = {(x1; X2; X3; X4) E R4|¤1 – *2+ x3 = 0 A x2 + x3 + x4 = 0}. %3D…

A: see below the answer and explanation

Q: Let Find a basis for the null space of A. A = -2 3-1 -6 9 -3 33

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Q: |Let -2 1 -3 A 7 -1 Find an orthonormal basis of the row space of A.

A: Use Gram -Schmidt Orthogonalization process to find the orthonormal basis of the row space of A.

Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.