Let B To which point do the linear maps associated with A and B map the points (1, – 9) and (4, 4)? Find the 2 x 2 matrix representing the linear map R? → R² that sends the points (9,9) to (19, 13) and the ponit (9,8) to (7,9).

Q: iv) Find a basis for ker(T). 1o lamsd zied v) Determine the dimension of the ker(T). vi) Find a…

A: Given Transformation convert to the matrix T(w)= 3-6  2-2 4  1 1-2-1-1 2  2 Transform the matrix to…

Q: Show that T(x1, x2, x3) = (3x₁ - 6x3, x2 + x3, x1 - x2 - 2x3) is a linear trans- ormation by finding…

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Q: The cross product of two vectors in R³ is defined by b₁ a₂b3 - a3b₂ 8-0-6-3 b₂ a3b₁ - α₁b3 b3 a₁b₂ -…

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Q: Show that the three points (x1, y1), (x2, y2), and (x3, y3) in a plane are collinear if and only if…

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Q: 5. Let B {(1,0). (0,1)) and B'-((-3,5). (4,1)) be ordered bases for R2 and let v = - Find [v]g, the…

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Q: Let A be an m x n matrix with columns C₁, C₂,, Cn. If rank A = n, show that {ATc₁, AT c₂,, ATc₂} is…

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Q: Suppose that T is a linear transformation from R2 to the space of 2 × 2 matrices which satisfies:…

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Q: Determine whether b is in col( A) and whether w is in row(A)

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Q: Let's create a matrix that reflects around a line that is perpendicular to the vector n = [0.375,…

A: Given Data: The given details are We want to create a matrix that reflects around a line that is…

Q: 3. Let T: R² R² be the linear transformation which first reflects points through the line X₁ = X₂…

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Q: Compute the standard matrix for the linear map T : R² → R² which (1) rotates i by 0 = T, (2)…

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Q: show that T is a linear transformation by finding a matrix that implements the mapping. Note that…

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Q: Let A = {a,,a2,a3} and B = (b1,b2.b3} be bases for a vector space V, and suppose a, = 4b, - b2, a2 =…

A: Given that A=a1,a2,a3 and B=b1,b2,b3 be bases for a vector space V, and given…

Q: Let T : R² → R³ be the linear map given by [2r1 + 7x2] 2i + 22 Write does the matrix A associated…

A: The given linear map is T:ℝ2→ℝ3Tx1,x2=2x1+7x2, x1-x2, x1+x2 To find the matrix A associated with T…

Q: 5. Show that T is a linear transformation by finding a matrix that implements the mapping. Note that…

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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.