1 3 - 1 4 - 5 - 5 Let A = 1 4 3 1 3 - 1 (i) Find bases for the RS(A) , CS(A) and the NS(A). (ii) Determine rank(A) and nullity(A).

Q: S-((1,1,0), (-2, 0, 1), (-1, 1, 1)is Not a basis ofR this is true O Linearly Independent Basis of R…

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Q: -1 1 -2 1 Find a basis for the row and column spaces of A = and find rank(A). 4 -2 3 -9- 3.

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Q: Let B = {(1, 1), (2, 3)} and B′ = {(5, 2), (1, 3)} be two bases for R2. [T]B= 2 3 4 7 (a) Find (T…

A: please see the next step for solution

Q: (2) Find an orthonormal basis of ColA, where 3 -5 1 1 1 1 A = -1 -2 3 -7 8.

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Q: 1 2 . Let uj = |0 u2 = 4 and u3 = 1 1 1 -2 (a) Show that {u1,u2, U3} is an orthogonal set.

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

Q: Consider the multiplication operator LA: R² R² defined by LA(x) = Ax where A = 6 [LAB= Hint: [LA] A…

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Q: 4 Let A = 2 -3 −1 1 -1 −1 9 1 02 (a) Find bases for the row and column spaces of A. Identify the…

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Q: /2 003 1Y 0-10 00 II-I0 (2 2 210,

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Q: 2 4 -2 -1 W = span({ 0 }) -1 -2 (a) Find a basis B for W. (c) Write down the dimension of W.

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Q: 8. Let B₁ = {[2][¹₂]} and B₂ = {[2¹][3]} 2 i. Find [1] B ii. Find [1] B₁ B2 B₂-1 iii. Show that…

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Q: Use elementary row operations to determine A-1 (you should be able to do (a) elementary row…

A: 1.a A=123-111201A=11-0-2-1-2+30-2     =1+6-6     =1determinant of A is not zero, therefore inverse…

Q: EXER 7: MATRICES Prove that if N is invertible then MN¹ = N¹M if and only if MN=NM.

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Q: Problem 3 Consider the matrix 1 -1 5 A = 2 7 -3 -5 -3 (i) Find a basis for col (A) and determine the…

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Q: Let b₁=(1). -(-9), --(-4), C1 = = (-3). {c₁, c2} be bases for R². Find the change of coordinates…

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Q: -1 -2 -3 -41 3 1 Let A = 1 11 Compute det (A) using the cofactor expansion along the first column.

A: A matrix is a mathematical object containing numbers arranged in rows and columns. The order of a…

Q: 7 Find w if (w)s = |0| relative to the basis S = 3 – 10 3 W =

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Q: Y1 y2 y3 y4 ys Y1| 0.9 0.3 0.4 0.1 0.2 0 1 0.7 V2| 0.2 1 0.8 R, (x, y) = x, 0.3 0.5 0 0.2 R, (y, z)…

A: Given data:                       y1   y2 y3y4 y5R1x,y=x1x2x30.10.2010.70.30.500.210.8010.40.3…

Q: (1 point) The matrices - [8]. [J]. -[i]·.^ - [i]· A A4 = A₁ = A3 = A₂ = form a basis for the linear…

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Q: 3) Let T d b }]= la + 1b + 1c + 5d + 2e +2f la + 2b + 0c + 5d + 3e + 1f 3a + 4b +3c + 17d+ 8e +6f…

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Q: (d) What is the nullity of [T]? (e) Give a basis for the kernel of T.

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Q: 1 1 1 -1 Given A = 2 1 4 2 -4 (a) Find bases for the row space and null space of the matrix A. (b)…

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Q: Consider the multiplication operator LA: R2 R2 defined by LA(z)= Ax where A = E is the standard…

A: Given, the multiplication operator LA:R2 → R2 defined by LAx=Ax  where A=031-2We have to find an…

Q: II Coordinates 5. Fix some a € R, and define polynomials Po(X), P1(X), P2(X) = P(R) by Po(X) = 1,…

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Q: (C) A rank of multiplication of two tensors of type (m1, n1, W1) and (m2, n2, W2) is (i) (ii) (iii)…

A: Option (III) is correct.

Q: - Create a table that counts from 0-100 in intervals of 18. - Look at the tensor below 29 0 -51] G 0…

A: Since, you have posted multiple questions but according to guidelines we will solve first question…

Q: Let A = {a, b, c, d} and let R and S be the relations on A whose matrices are (1 0 1 0) 1 0 0 1 1 0…

A: The set is A = {a, b, c, d}. The matrices representing the relations R and S, respectively, are as…

Q: Discovery 4.6. Consider 1 -3 -1 A = 1 3 %3D -2 2 3 -1 -2. Compute the product AX by considering X as…

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Q: If L and U are invertible, then (LU)²001-U001L001 Find A001 from the given LU factorization: = -2 0…

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Q: Consider the basis a = {1,1+x, 1+a+x ?} of P 2(R), and suppose 8 is another basis such that the…

A: Please look at step 2 for solution.

Q: Let S P₂ P₂ be the linear transformation where S(x) = -12x - 30 and S(1) = 5x + 13. 0 Suppose Mg(S)…

A: Let,      B = {x + a, x + b}  Now,        S(x + a) = S(x) + aS(1)                       = -12x - 30…

Q: Find a basis for (null(B))+, where 1 2 -1 -3 2 2 4 -2 1 4 B := 1 2 3 -1 -2 1 2 11 -11 -10

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