Suppose that T : R2 --> R2 is linear, T(1,0) = (1, 4), and T(1, 1) = (2, 5). What is T(2, 3)? Is T one-to-one?

Q: Which of the points P = (-1,4,-7) and Q = (6,-1,5) is closest to the z-axis? OQ (6,-1,5) OQ (6,-1,0)…

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Q: Find the constants m and b in the linear function y = f(x)= mx + b, such that f(1) = -2 and f(3) =…

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Q: Solve for the orthogonal traysctories x*(3k-x) - ky². = x ? 2

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Q: Find eqation of line through the point (4,2,1) and (0,4,2)

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Q: -t,x-1 dt

A: Please see the explanation below

Q: Let ā = (1, 3,-1) and b (-1,0, 2). What is the y-component of ā x b %3D %3D 1 -1 3.

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Q: Given the function g of the two real variables t and u by g(t,u)=t^2 + tu-u^2+(6+2)u c) Determine…

A: Linearization of a function g(t,u) about (a,b) is  L(t,u)=g(a,b)+(t-a)gt(a,b)+(u-b)gu(a,b)

Q: Suppose a firm's technology is represented by the production function f(L, K) = min(L, 2K), where L…

A: As we know that all isoquant curves are strictly negative sloped hence, if one of the point is (4,…

Q: +3. . Find the linearization of _9). Can you tell anything about the error? at (3,2). Evaluate at…

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Q: Suppose that a = xdy is a 1 form and Y(v1, v2, v3) = ((v1 – v3)² (v2 – v3)²) ædy what is "a ?

A: Given α=xdy-----(i)γ(v1,v2,v3)=((v1-v3)2,(v2-v3)2)---(ii) To find γ*α------(iii) from (ii) we…

Q: Use least-squares regression to fit a straight line y = f(x) = Ax+B  to:   xi -8 -3 0 4 6 yi 7 4 2…

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Q: The linearity between two variables X and Y, in pairs, defined as X=[4,2,3,5,2,4] and…

A: Linearity x y xy x2 y2   4 6 24 16 36   2 4 8 4 16   3 6 18 9 36   5 8 40 25 64   2 5…

Q: Determine whether u= (-1, 11) is a linear combination of x =(1,3) and y=(2,-1).

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Q: Calculate the length of PQ where P = (-2,1,6) and Q = (-3,4, –1).

A: We will find the length of PQ→ in the following step

Q: Find the points of intersection of x = 4y and y = 4x. (ans.:(0,0),(16,64))

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Q: If A = 3a_0 + 2a_0 - 5a_z and B = -2a_p + 3a_0- a_z are given at points P(3,T1/6,5) and Q(4,T1/3,3)…

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)…

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Q: If f.(x, y) = 13x + 8y + 11, || f.(3, 2) = a. b. f„(5, 2)

A: Given, fx(x,y) = 13x + 8y + 11 a). fx(3,2) = 13*3 + 8*2 + 11 = 39+16+11 => fx(3,2) = 66

Q: Find the orthogonal trajectories of the family of lines 3x + 5y = C (A 3x - 5y = k (B 5x + Зу - k ©…

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Q: If A = ( - 1, 2) and B = (3, 4), find AB and redraw it (a) in standard position and(b) with its tail…

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Q: If A = x²zi + xyj + y²zk and B = yz²i+xzj + x²zk determine the expression grad(A.B) at the point…

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Q: 1. Is L = {1 − 2x + 3x^2, x − 2x^2, 2 − 5x + 8x^2} linearly independent? If yes, show why. If not,…

A: Given:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.