Vector v1=[1, 1, 2]T, vector v2=[0, 1, 1]T, vector v3=[-1, 2, 0]T Transformation f : R3 -> R3 is given by the pictures of vector v1 v2 v3 as follows: f(v1) = [-9, 6, -3]T ,f(v2) = [-3, 2, -1]T ,f(v3) = [5, -3, 4]T Find the matrix transformation f relative to the base unit Find, if vector u = [-1, 2, 1]T is in the core of this transformation

Q: A vector has initial point (−11,−12) and terminal point (20,−19) The component form of the vector…

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Q: Point P₁ lies on the line {₁:[4,4,-3]+t[2,1,−1],tER, and point P2 lies on the line…

A: Solution : Given that the lines l1 : 4,4,-3+t2,1,-1l2 : -2,-7,2+s3,2,-3

Q: Let T: R2 R be a reflection in the x-axis. Find the image of each vector. (a) (7, 6) (b) (9,-3) (c)…

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Q: Find the vector equation of the line through the points P0(x0, y0, z0) and P1(x1, y1, z1).

A: P0x0, y0, z0 & P1x1, y1, z1. Now let a→ & b→ be the position vectors of the points P0x0, y0,…

Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Find the vector and parametric equations of the line through the points A = (2,4,7) and B =…

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Q: Sketch a graph of each vector. 11) b=(-2V2,-1) 12) RS where R= (-6, 1) S= (-8,-10)

A: Solution (11.)

Q: X = Find the vector equation for the line of intersection of the planes x - 5y + 5z = −5 and x + 5z…

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Q: Given the points A: (-5,4,0) and B: (2,-2,4), find the vector u = AB ú=< -3 X 2 X 4

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Q: (a) Find a vector equation and symmetric equations for the line through the point (0, 14, 10) and…

A: Approach to solving the question:We are given a point (0,14,10) and a direction vector d=(2,−3,9).…

Q: Vectors a=(;) b=(;) c=(?) 2a + 3b + 4c = (

A: So here we have to add the matrix by multiplying given conditions so I'm providing hand written…

Q: p1-2-is-the-image-of-p-after-a-translation-along-the-vector-8-0.-what-are-the-coordinates

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Q: Express the vector v with initial point P and terminal po P(-9, -7), Q(-3, -3)

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Q: Let L₁ be the line passing through the points Q₁(-4, 5, −5) and Q₂(−1, 6, –2 and let L₂ be the line…

A: This is a question of 3D geometry and vector analysis.

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.