Given that a₁ = a2 A -2 3 and -2 -2 -11- 0- 1 1 and 1 -3 = [a₁ a2 a3 a4 ] and has U = RREF given by 1 0 0 0 1 = 7 -1 2 -5 0 0 00 00 00 00 Knowing that relationship among the columns do not change under RREF, find out what the relationship among the columns of U are,build the relationship among the columns of A, use them to construct a3 and a.

Q: Let a = - 2ỉ - 4j – k and b = 4j + 2k. Find — ả + b. V

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Q: Find the values for c1, c2, and c3 to make sure that: c1 (10, 25, 1) + c2 (-15, 5, 0) + c3 (5, 0,…

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Q: Find minor and cofactor of the first row and then use them to find 3 -7 -1 0 -8 8 2 3 -7 -1 = Choose…

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Q: 3 Let A= (MA-|| _23]~B-[2²] and = 6-9 -4 -6 Find - 2A + 2B. - 2A + 2B=

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Q: A=[[3,2],[7,5]],B=[[2,6],[3,9]],AB=[[a,b],[c,d]] Determine the values of the entries in the product…

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Q: 8. (S.15). Write P20 r2+2r-1 as a linear combination of the polynomials P21 r-r- 2, P22 2r2-r+3, P23…

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Q: Let B = [-1 1 4 -3] Find -4B

A: Solution

Q: Find A x Bx C where A = {4,6},B={14,18} , C = {0}. O (4,14,0), (4, 18,0), (6, 14, 0), (6, 18, 0) O…

A: given A={4,6}B={14,18}C={0}

Q: Find A x B x C where A = {2, 5}., B = {13, 17}, C = {0} . O (2,13,0), (2, 17,0), (5, 13, 0), (5, 17,…

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Q: Find the rank of A = ( 1   -1   2   3)                                       2  6  -8   1…

A: Rank of Matrix : It is the Number of Non Zero rows in reduced row echelon form.

Q: GIven u = and v = determine -4u - v

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Q: B бх +7 4x -3 A4 Зх + 16

A: Answer

Q: T. If TM 3y and TX 2y + 24, then Y

A: Given,  TM = 3y TX = 2y + 24

Q: Find A. A = (2A)-1 [ -1 -2 2 2

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Q: Find the LU factorization of A = A = 1 1 -3 0 9 3 -17 5 2

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Q: Let ā = (– 2, – 1, 3) and b = (- 5, 1, – 4). Find ā · b.

A: Given that , a→=-2 ,-1 ,3 and b→=-5 ,1 ,-4 a→·b→=?

Q: -1 -4 -1 5 21 A -2 -5 -14 4888|16 Find the LU factorization of A = A =

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Q: Find the polynomial that interpolates the points (-2,4), (-1,0), (2,-1), (2.5,0), (3,1), (4, 2). Use…

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Q: Find a + b, 2a + 3b, lal, and la - b|. a = (4, –3), b = (-2, 5) a + b = (9,2) (2,9) 2a + 3b =

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Q: Write as a line ar Combination of V, ,Vz,V3 where V= (1,5,4) ,V, =(1,3,-2),Vz=(2,7,-1) Vz=(1,6,7)

A: The given vectors are: v=1, 5, 4, v1=1, 3, -2, v2=2, 7, -1 and v3=1, 6, 7 Write the vector v as a…

Q: Suppose A = (-1, –5, –7) and AB= (-5, 14, 4). Then В — (5,-70,-28) help (points)

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Q: Given w= (-4, 12), s=(-6, -2), and r=(4, 11), %3D find 6r-(w+s). 6r-(w+s) =(| , O)

A: This is related to vector addition sub, and mul

Q: Find a × b if b = (–6, 9, —15) and à = (4, −6, 10) (-3,-2,0) (0,0,0) (1,-1,-1) (-24,-54,-150)

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Q: stitution? I have to use the Column Correspon

A: Is (1,2,3,4,5,6)∈ span( (1,1,1,1,1,1),(0,1,0,1,0,2),(6,5,4,3,2,1)) > A x1 x2 x3 x4 x5 x6…

Q: Consider the relation on A = {a, b, c, d, e} given by R={(a,b),(b,c), (b,d),(b,e),(d,

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Q: Suppose an = -3an-1 a1 = a2 = a3 = 2an-2+ 6an-3 and a4 = -17, a5 = 53, and a = -167. Find a₁, 92,…

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Q: Find the value of a, b, and c if (a+b)(a+b+c)=21, (a+c)(a+b+c)=35, and (b+c)(a+b+c)=42.

A: First we need to make some equations and the we have to simplify them in order to get a, b and c.

Q: Let a = (1, 3, 8) and b = (7, 3, 4). Compute 5a + 7b

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Q: Suppose the second column of B is all zeros.  What can you say about the second column of AB?

A: If the second column of B is all Zeros, then the second column of AB will also be all Zeros.

Q: 3. Find both linear and quadratic interpolating polynomials for the points (-2,-13) , (-1,-3) ,…

A: We take given pairs of points as (x, y) x y -2 -13 -1 -3 1 -1 2 -9 3 17 We have…

Q: Find whether A and B are independent in the following cases : (AB) = 256 ; (aB) = 768 ; (AßB) = 48 ;…

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Q: Calculate the linear combination: 1 (2, 2, –4) + 4 (-2, 3, 2) = %3D

A: Linear combination of a set of vectors: Let us consider V be a vector space over the field F. Let…