1. Let A = (a) (b) -3 6 11 4 1 3 21 5 6 1 1 5 16 -15 15 You may use that rref(A) = Find a basis for im(A). Find a basis for ker(A). 5 0 1 3 -4 0 000 0 1 000 0

Q: Consider the following linear transformation of R³: T(F₁, F2, F3) =(-2-₁ −2 - x₂ + x3, 2-₁ + 2x₂ −…

A: Tx1, x2, x3=-2x1-2x2+x3, 2x1+2x2-x3, 6x1+6x2-3x3

Q: 1. Answer the following for the given equation Ax = 0. (a) Find a basis for ColSp(A). (b) Find a…

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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: Verify that each basis vector of Null(A) is orthogonal to every basis vector for row (A) Find a…

A: Given the matrix ,where B=rref(A).We already have seen that the basis for nullspace of A is And, the…

Q: 4 1 7 - - - - H -3 V2 = 9 14 11 , and also let H = Span{v1, 02, 03}. 7 -2 6 It can be verified that…

A: It can be verified that Using this information we have to find a basis for H.

Q: -6 -2 -2 0 -6 -2 -2. Find a basis for N (A), the null space of A. Let A = [ 0

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Q: DO NUMBER 5 (Linear Alegbra & Diff. equations)

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Q: Assisted Computation: For each item, you are given a matrix A, its rref R, and the of A". (i) Find a…

A: Since there are multiple questions with multiple subparts. So we'll solve first question having…

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: 201 2 3 11 10. Let A 3512 (a). Find the reduced row echelon form of A. (b). Use the result from (a)…

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Q: -1 1 4 Let A = -3 3 12 -4 4 16 Find a basis for Null(A).

A: We are given a matrix of order 3×3 A= -1 1 4       -3 3 12       -4 4 16

Q: 3 1 . A = 1 1 1 1 -2 -2 -2 0 -4 -2 (a) Determine rank A and dim Nul A and justify your answer. (b)…

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Q: 4. Let A = [1 1 1]. Find a basis of N(A) and C(A).

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Q: Define T:R-→R² by T(x) = Ax. Find a basis B for R² with the property that [T]B is diagonal. - 3 - 3…

A: Given:T:ℝ2→ℝ2 is defined by Tx=AxWhere A=-3-3-1-5To find basis B for ℝ2 such that TB is diagonal.…

Q: 15 tig = 12 0. 6. form a basis for R if and only if k #

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Q: explain this answer for part c, im confused by it.

A: Step 1:Step 2:

Q: Consider the following two ordered bases of R3: B {(1, –1, –1), (–1,0, 1), (1, –1, –2)}, C {(2, –1,…

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Q: -2 1 4. Let v, = 4. 0 ,and v3 -4 Is {v1,V2.V3} a basis for R? V2 = %3D 0. %3D %3D -4 - 4 - 4 O No…

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

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Q: 12 69 -9 -12 -6 -8 11 28 4 6 3 Let B-3 (a) Find a basis for ColB. (b) Find a basis for RowB. (c)…

A: Our first target will be to reduce the given matrix in Echelon form by using elementary row…

Q: 11. Jack and Jill took a linear algebra exam. One of the questions was the following: Question: Let…

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Q: 1 -1 -4 3 -4 0 A basis is {v1, v2} where Let A 5 V1 || - Find a basis for Nul(A)+. V2 C

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Q: Find a basis for the column space of A

A: Column space of A = Span of columns of A = set of linear combination of the columns of A

Q: The union of these two orthogonal bases (put the basis for W and W- into one set) is an orthogonal…

A: Since you have asked for part (d) and (e) , so i answered here only for part (d) and (e).

Q: Show your work / explain your reasoning! - 1. Let W = Span{(2, –3, 0, 1), (4, –6, –2, 1), (6, –9,…

A: Note: We are entitled to solve only one question at a time and up to 3 sub-parts only. As the…

Q: 2]

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Q: 1 Let A = -3 0 -3. Find a basis for Col(A)+. 3 1 U1= 2 5 A basis is {1} where Dreview 20

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Q: 7 -5 9 4 3 3 -1 2 3 1 Let A = 1 -3 0 1 0 3 -1 7 0 2 (a) Find a basis for the row space of A, and…

A: The given matrix is as follows: A=7-59433-12311-30103-1702 (a) We are asked to find the row space of…

Q: -2 5 -3 1 1 2. Let S = 5 -1 7 Find an orthonormal basis for the space spanned by the -3 -2 -10 -1…

A: Given matrix is: S=-25-3110-175-3-2055-10-1

Q: -3 4 6. 6. 10 Find the rank(A). (For practice find a basis for the Let A %3! -3 6. -6 -6 -3 3 -9 4.…

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Q: See picture

A: Does the set L of two vectors form a basis for the subspace S?

Q: -2 -11 TO 1 The coordinates [Aleof A= with respect to the basis B= 0 -1 ] 2 of M2x2 O a. -1 -2 O b.…

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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: Find a basis for the nullspace of A.

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

Q: (a) Why is the set S = {(2,1, 3), (0,3, 2)} is not a basis for R'. (b) Why is the set S = {1, 4t, 5…

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

A: The given matrix is a 4x4 matrix. To find the basis for the null space of the matrix following steps…