0555 if A = 0 0 0 0 then the basis fqf 0 205 N(A") is 1 .a Hạmmad Selawe .b كواے 1 .c 0.

Q: 3. Let A = a. b. 1-2 3 1 1 1 Find the Null space of A. Find a basis for Null space of A. c. Find the…

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Q: 2 Consider the bases B₁ and B₂. 2 -3 -7 4 {{³][])} {₁ 6 -5 B₁ = Find [x]B₂ if [x]B₁ 2 [²]. 6

A:

Q: Explain why S is not a basis for M2,2.

A: Let's check if S is linearly independent or not. S will not be linearly independent if for some…

Q: 5.) Let B = {(1,1, –1), (1,–1,1), (-1,1,1)}, and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R³,…

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Q: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

A: Explain why S is not a basis for P2.S = {1, 2x, −4 + x2, 5x}

Q: [2 1] 4 and B := [o 3 Let A := 3 Find: (a) AB (b) BA

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Q: Let A = and v= Verify A(u + v) = Au +Av. 2.

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Q: What is the simplified form of 6. 21 ? А А Зу14 B 14 /3 С 21 D 63

A: We have to simplify

Q: Determine whether the set of polynomials 10. i (I+ x2, x + X2, 2 t x} is a basis forr Pe (TR).

A:

Q: 7. Which of the following are linear combinations of = (0, -2, 2) and v = (1, 3, –1)? (a) (2, 2, 2)…

A: For a,

Q: 01 find 22and 22 find 07 for we xtesny, awit,), 2w ) %3D he

A: z=xyx2+y2

Q: N(a + bi)N(c + di) = N[(a + bi)(c+ di)] = 2. Show that 65 can be expressed as a sum of two squares…

A: See the detailed solution below.

Q: - Determine if S = {[1246]} 0 forms a basis for M2,2.

A: We know that M2×2 is a vector space of all 2×2 real matrices over R.Given that .We need to determine…

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: 1. 4 -2 3 Compute A- 513 and (51 )A, where A = -4 4 -7 3 1 A-513 = %3D (513)A =

A: To find - Compute A - 5I3, and 5I3A, where A = 4-23-44-7-311

Q: [4 5 9 -2 1. Consider A = 6 5 1 3 4 8 -3 12 (a) What is Nul A? (b) Find a basis for Nul A. (c) What…

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Q: –10 S = l2] ] 13 2. 2.

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Q: 20 3x

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Q: 6.4 find an orthogonal basic

A: The orthogonal basis is given as follows :

Q: 2 1 0 If ɛij= 1 20 then the invariants are 0 0 2 I1= 6,12= 11 ,I3 = 6 .1O I1= 6 ,I2= 10,I3 = 6 .11O…

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Q: 9. Let S = { (1,2), (4, 5), (0, 2)}. Check whether S is a basis for ?2?

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Q: What is the formula for the {nk} in the Newton basis?

A: We need to specify the formula for the {nk} in the Newton basis

Q: tind the resolvent kernel and Solut of yox) = + by Alternative procedure

A: We have to solve the given integral equation by finding the appropriate kernel function.

Q: 41 1 -1 -8- 1 3. -2 Find the basis for the column space of -2 -6 4 a. {0 C. a 3. b. { d. {-1

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Q: Let 7(u,v)-(u, v, u+v), then the second fundamental coefficients are: 2 1+4u+4v² ,M= V1+4u+4v a O 2…

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Q: Let }].,)} 3 B = { 1.E be basis for IR %3D 2 Is B orthonormal ? False True

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Q: Determine Го A = 4 7 -1 6 -6 3 A11 = M11 M12= M13= M21= M22= M23 = M31= M32= = amma all minors and…

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Q: - Derive formulation for the elements of c(m, m') modified Daniell Kernel

A: Given information: The information about modified Daniell kernel is given.

Q: Verify that (AB)T = BTAT.

A: Now,

Q: [4 5 9-21 1. Consider A = 6 5 1 12 3 4 8 -3 (a) What is Nul A? (b) Find a basis for Nul A. (c) What…

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Q: 1 1 5 1 2-i + 5i 1+2i oVerify that: (1) (2) 2- 3i +i 26 26 3- 4i 3 i 30 – j19 (3) 21 -1 (4) i (1-J3…

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Q: Find JA|, IB|, A + B, and |A + BỊ. Then verify that |A| + |B| # |A + B|. 15 0 1 -1 A = 1 -1 0 B = 5…

A: topic - determinant and matrices

Q: Basis 6. 10 9. X1 X2 X3 X4 X5 X6 minß,(8) X4 120 3 15 5 1 8,00 x5 120 18 1 12,00 X6 36 4 6 1 9,00…

A: We have given the iteration tables of obtaining the optimal solution using simplex method. Simplex…

Q: - --- Let B = Is Ba basis ofR ? Justify and x = %3D 2 3 3 your answer. If yes, compute xR [x]

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.