Show that T is a linear transformation by finding a matrix that implements the mapping. Note that x,, X2, ... are not vectors but are entries in vectors. T(X1,X2.X3) = (X1 - 3x2 + 2x3, X2 - 7x3) A = (Type an integer or decimal for each matrix element.)

Q: Determine whether the given set is linearly dependent or linearly independent: S =

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Q: Find a base for the line space of the matrix and determine the line rank.

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Q: Identify the matrix that represents each linear transformation below. Write A, B, C, D, D or F. ^ -…

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Q: Find the equation of the line that passes tru the points (-1,-3) and (5,1)

A: Given points are: (-1,-3) and (5,1) Equation of line: y-y1=m(x-x1) Where (x1,y1)=(5,1) m=slope of…

Q: Show that the inverse of an invertible lower triangular matrix is lower triangular

A: Given : The matrix A is an invertible lower triangular matrix Then we have to show that A-1 is…

Q: -1 find its inverse A¬'. Check that your inverse is actual in 2 For a matrix A = -3 Ichow vour work…

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Q: What is the rank of the matrix?

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Q: Construct six linearly independent 3 by 3 echelon matrices U1, ... , U6.

A: To Find : Construct six linearly independent 3×3  echelon matrices.

Q: 3 4 Let X and Y in the set of 2 × 2 matrices, M22. %3D -11 2 3 Determine whether A = or B are in…

A: Given  X=2-121, Y=34-11 and A=0-1181, B=2312

Q: Find the projection matrix P, and the projection of b= (1,2,3) onto 2. Let A= -1 -1 the column space…

A: Given matrix is A=1001-1-1

Q: 9. Show that the matrix 0 0 -1 0 0 1 -1 C2 = x, x- will transform the vector y into -y

A: We have to show that the matrix C2 will transform the vector in ℝ3 into the vector -x-yz. First we…

Q: Explain  column vector of m x 1 matrix?

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Q: let Q(x)= x12 -8x1x2 -5x22 , then matrix A of the quadratic from is A=?

A: Explanation is given below..

Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

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Q: Suppose A is a 2 × 4 matrix, and B is a 4 × 2 matrix. Assuming that A, B act on vectors in R",…

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Q: Let B=(b₁,b₂), C=(C₁,C₂), be bases for R² b₁ = (-5,-3), b₂ =(3,2), C₁=(1,3), C₂ = (1,2) Find the…

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Q: Show that the inverse of a nonsingular lower triangular matrix is lower triangular.

A: We have to prove that inverse of a nonsingular lower triangular matrix is lower triangular.

Q: Use the definition of A to write the vector equation as an augmented matrix. 0 x₁ + x2 + x3 + X4 =

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Q: Exercise 51. Is there a square matrix X with real entries such that det(X¹X) = -3?

A: detXTX=-3 X is a square matrix with real entries.

Q: Find the general form of the span of the indicated matrices. (Use only x and w as variables in your…

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