Show that ||T(x)|| = ||x||, Vx E R². Show that T(x) · T(y) = x · y, Vx € R². Interpret the property (a) in terms of geometry.

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: (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: Find (if it exists) the inverse of B where B = |0 1 1 1 1 1 1 0001 0 0 1 1

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Q: Ww.3.10® Expess E Expess i 5 as a livear combination of 2 and Vo

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Q: An economy is based on three sectors - agriculture, manufacturing, and energy. For each unit of…

A: According to the given data, determine the intermediate demands:

Q: [-3 -2 Let A= 0 -6 and b = 14 3 2 6 Determine whether b is in the column space of A.

A: If b is in column space of A then Rank (A:b)=Rank(A).

Q: Determine whether the transformation is one-to-one. I1 +2 - 13 + 2x4 +4x5 -201 - 12 + 2x3 – 3x4 +…

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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…

Q: Let 2 -1 1 -4 4 A = 1 2 1 3 2 Find M22 and C22. 6

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: 4. If three dice are rolled, what is the probability that a 1 will appear on each die?

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Q: -1 – 7 -3 (a) Let A = 15 6 Find the second column of A-1 without com- 1 3 puting the other columns.

A: Given,A=-1-7-32156132

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.

Q: Find BA. A= BA= 0 -:] 7 -1 -3 0 -3 -5 -4

A: Finding the product of matrices.

Q: Which transformation should be use to make the equation = xy-3, y(1) = 2 linear? O a. y³ = v O b.…

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Q: 4 1 4 1. Is (2) Col (2-¹); E -8 ?

A: Introduction: Column Space of a Matrix:The column space of an matrix A is the span of the columns of…

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

A: Given: 1231351512

Q: 7 10 0 3 9 5 [E] = -4 4 3 [D] = 4 8 -3 -5 1 2 -6 -7 -8 3[E] – 2[D] =

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Q: Let A and B [1 27 show that A and B are not similar. 0 1

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.