The dimension of null space of A 123 4 5 6 for A-1 49 16 25 36 49 18 27 64 5 46 343 and 20 100 0 -1 -4 0100 4 15 R-o 010-6 -20 10 0 0 014 10 -14

Q: "(A v B) A -(A - B)" is valid O unsatisfiable satisfiable O undecidable semidecidable O unsolvable

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Q: 1 2 The rank of A =|0 1 is 2 4

A: We can find the rank as below.

Q: А понерне об mension of each ? A= 52 Зо -1322 Ч 21 з

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Q: Let 1 0 -2 1 0 0 -1 -3 1 3 %3D -1 1 -1 1 3 0 -2 3 -4 Then nullity (A) O None 3 2 4 1.

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Q: [1 2 -3] Find det A A= 4 5 -9 0 1 0]

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Q: (1 1 2 2) Let A = 1 2 3 1,v1 = 1 3 4 0, v2 = Which amongst vı, V2, V3 is an element of null(A)? a)…

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Q: a) range 1 0 0 11 00 10 b) range 1 1 01 1 c) span ((1,-1, 1), (−1, 1, 1), (1, 1, −1), (1, 1, 1)) d)…

A: Note : '' As per guidelines we will solve first three subparts. If you want any specific subpart to…

Q: 7 - 32 0 - 36 ? -4 1 Is - 4| in the null space of A= 9 2 3 - 4 Is it in Column space of A?

A: Suppose A is any mxn matrix then Null(A) is the collection of all vectors y of order nx1 such that…

Q: Find a basis for the Null space of 10 -5 3 0 1 -2 5 5 -13 1-50 A = 0 1 a. {(5,2,1,0), (-3, -5,0,1))…

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Q: (3) Consider the sequencex + 3,x + 7,4x - 2,.......... (a) If the sequence is arithmetic, find x and…

A: As per our policy I can solve only one Question. Kindly please repost the Q4

Q: 20 2 Compute det B* where B = 113 2 2 2

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Q: Determine the null space of A and verify the Rank-Nullity Theorem. 1 -4 9 9 -7 A = -1 2 -4 1 5 -6 10…

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Q: Let V be the set of all ordered pairs of real numbers under the following operations of addition 1.…

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Q: 2 3 2 If Eij= 3 -1 5 then the invariants are 25 -4 I1= -7 ,I2= 12,I3 = 50 .I %3D I= -1, I2= 12 , I3…

A: Given that,

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 A = 12 3 14 0 1 02 -3 0 1000 What are the rank and nullity of A?

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Q: Let A = [1111;0101;1212;0-10-1] = [1 11 1] [0 10 1] [1 21 2] [0-10-1). Find bases for the column…

A: Given:-                    Given matrix                                           A =…

Q: Write the following equations using index notation and Einstein summation convention: (a) (a b)(b c)…

A: The following are the rules in the Einstein's summation convention having the index notation:1) The…

Q: -12 2 Find a basis for the null space of A = 60 -10 1 Ex: 1

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Q: [2 6 2 B = |4 6 0 -21 ; Determine a basis fot he column space of B. 2 L2 0 4

A: Given that, B=262-246022040 We need to find the basis for the column space of B.

Q: Given the following fuzzy relations 0.2 0.4 0.6 R₁: 0.1 0.9 0.0 0 0.4 0.8 Compute the following 1.…

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Q: Find a basis for the null space of 1-1 3 3 2

A: We have to find the basis for null space of 1-13324 Definition : Null space of A is defined as…

Q: Suppose S={1+ 3z , 1-4x*}. wh.ch of the pollynomiais given Could be added to the set S to form basis…

A: We know that any 3 Linearly Independent vectors form a basis for P2 . Hence we have to check whether…

Q: [1 3 1 -1 Let A = |0 1 2 3 -2. Which of the following sets is a basis for the null lo o 1 4 space of…

A: Let ,  A = 131-100123-200144 We need to find Basis for null space of A. For that , first we will…

Q: let 4 be a Hilbert space and s, and so be any two subset of H then (3) {o? ² = H (") SAS+ = {0} 9,…

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Q: -3 Let A = -1 -12 -5 5 20 -47] -21 80 Use the fact that det (A) = 5 to compute -6 -2 10 -10 40 -94…

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Q: 4 -3 v1 = V2 %3D form a basis for IR if and only if k

A: Solve the following

Q: 2. Show that if vER is a vector and that a ER is a real number, then v^ (av) = 0

A: We shall answer the Que in next step using exterior product or called as wedge product. We also…

Q: Examples 2 then 2: Prove: If If x<y <y+v. x + M and u<v

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Q: 2]

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Q: 2. Find a basis for the null space of 1 -204 A=0 01-9 -90 0 000 1

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Q: One of the following is an axiom of 2 points the definition of the Pre-Hilbert space =- =+ O =-i

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Q: 4 -1 4 33. The dimension of the null-space of A = 3 2 is 2 1 1 1 2 3 (A) 1 (B) 2 (C) 3 (D) 0 (E) 4…

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Q: 17 Find three different bases for the column different bases for the row space of U. space of U =…

A: Given, matrix  is U

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.