Let 10 1-1 0 A = -2 1 0 1 -1 0 1 02-1 -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: 1 4 A basis for H =Span is: -1 1 -4 4 -1 1 1 -4 1 -1 1re 1 1 0.

A: Basis of a vector space is maximal linearly independent suset.

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 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: 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: XI Let W = X2| 0 2X1 -X z+ X4= + Xy = o] be a subset of Rt IRt. which one is the basis for W?

A: Given W=x1x2x3x4:2x1-x2+x4=0 be a subspace of ℝ4

Q: Find a basis for the null space of matrix A. [3 4 01 A = 1 2 1 Basis is

A: Let's find.

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 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: 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: Find a basis for the null space of the matrix. [10-40-4] 01 20 2 A-00 01 1 0 00 00

A: Given matrix is A= 10-40-4012020001100000. To find  a basis for the null space of the given matrix.

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: 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: 0 1 3 let A = -1 0 1 -1 27 Then a basis for the nullspace of A is none 3 1 -3 3 1 2

A: The answer is option C

Q: 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.

A: see below the answer

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: 1 Let A = 1 d where c, d denote real numbers. 0 0 0 3 If a basis for im(A) is and a basis for…

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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 -4 -1 7 -11 3 -1 A 13 -1 1 -3 13 -1 1 -3 Find orthonormal bases of the kernel and image of A.…

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Q: Let A = {(4,1,0); (1,0,-2); (0,1,-5)}. Then A is a basis for

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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 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 [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: 2 1. Find a basis of the null space of the matrix B -2 -2 -4

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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: 6. Find a polynomial p(x) for which {r² – 1, x² +x +2, p(x)} is a basis of P2(R).

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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: I Let 6 A = --2 -2 -4 -2 -2 -4 Find a basis for the null space of A. {

A: Let us consider matrix A of order n x m. The null space of matrix A is defined as: Null(A)=x∈Rm|Ax=0…

Q: [3 9 5 : A=0 4 0 1 00 0 0J Find a basis for the null space of the matrix.

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Q: Let 1 -4 A = -2 2 6 3 10 Find an orthonormal basis of the column space of A.

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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: 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: 4. Find a basis of the nullspace of 2 -6 5 -8 A = 1 -3 1 -1 3 -9 4 -5

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

A: The answer is:  (A) S is a basis of P2. Proved below.

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: 6

A: Consider the provided matrix, First find the row echelon form of the given matrix,

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: 1 0 11 let A =| -2 1 10 7 -2 1 3 The basis for rowspace of A

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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.

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.…

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.