2 Define T: R2 → R? by T(x) = Ax. Find a basis B for R? with the property that [T], is diagonal. - 6 A = - 5 4 A basis for R? with the property that [T], is diagonal is { }. (Type a vector or list of vectors. Use a comma to separate vectors as needed.)

Q: a₁a₂ a3 b₁ If b₁ b₂ b3 = 1, then a₁ C1 C₂ C3 A-2 b₂ b3 a2 a3 20₁ 20₂ 203 B8 = C2 D-8

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Q: -1 0 12 0 1 0. -3 -1 12 1 -3 -3 Ans. -1, ;-5, ; 3, -1 -4 1 1 -4 -1 1 3. ..

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Q: (o42)2) O 3te-24 O 3e 4 (1 + 2r) 3e-21 O 3e-24 (1 – 21) O 3e4 (1 + 2t)

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Q: 3 -3

A: An important fact about elementary matrices is that if a matrix A is invertible, then it can be…

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A: Given matrix is: A=2-11600-4421052132

Q: {x ER: 2x + 31+x=0} = {-6, -2}

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Q: [ 5 8 . Determine x and y if: ]3 4] 23 34

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Q: 0 1 2 3 4 -1 -0.5 0 -0.5 -1 is this linear?

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Q: 2 2] 2. Solve for x, y and z. -5 6

A: We will solve the problem

Q: a12 ain a21 a22 a2n C2 and c = then express the product Question 2(a): If A = Cn Am2

A: The given matrices A and C are: As in matrix A has "m" rows and "n" columns and in matrix C has "n"…

Q: 2 -2 If B = then B is not invertible. -3 3

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Q: 1 2. Can c = 1 be written as a linear combination of a1, a2, a3 ? explain why or 1 why not?

A: Step 1:

Q: Find the two conditions on b1, b2, and bz which determine solvability of 4 8. 3 4 =6= b2 -6 -7 -8 b3

A: The objective is to form the equation involving b1, b2, and b3 that determine the solvability of the…

Q: det b2 a1 92 261 262 b1 b3 az 2b3 + det C2 a1 92 2b1 262 C1 C3 az 263 = det b₁ b2 b3 a1 a2 a3 + det…

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Q: a2 аз ад 1. The value of BA if B = [1 0 0] and A = |b1 b2 b3 b4 [C1 C2 C3 C4

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Q: 3 . If 4C + 2 [10 0 , find C. 4 2

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Q: da

A: Given integral is, ∫-40(4.4x2-1)dx=∫-404.4x2dx-∫-401dx=4.4[x33]-40-[x]-40…

Q: dw V5-e-2w

A: Given,           ∫dw5-e-2w

Q: Find a diagonal matrix D and an invertible matrix P such that A PDP-1

A: Given matrix , A=101012002 To find: diagonal matrix D and an invertible matrix P . Let, λ be the…

Q: Question 16 Evaluate: (A +C 글지(Sx + 3) +C В C 2x D x++x ]+C

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Q: [1 -2 -1] Let A- 2 4 l3 0 -2 -1 3 and B- 3 2 . Express the second column of AB as linear…

A: The objective is to express the second column of AB as linear combinations.

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A: Finding the product of matrices.

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Q: 1   2    3 Find the inverse of the matrix=  1   3     5…

A: Given: 1231351512

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A: To check the similarity of the matrices, calculate the determinant of the matrices A=1001 and…

Q: Given B = v1 {(0, 1, 1, 1)}, v2 = {2,1, –1, –1}, v3 {(1,4, –1,2)}, v4{(6,9, 4, 2)} B' = wi {(0, 8,…

A: In this problem we used Gram-Schmidt orthogonalization  process.

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.