2. Let T: R³ → R² be given by (E)- 3x1 + 2x2 4.x2 – 5x3 T = and let L: R → R³ be given by 6x1 + 12 -3x2 L (a) Show that T and L are linear transformations by showing that they are given by matrix multiplication. (b) Find the standard matrix for the composition LoT.

Q: Q: Determine if the following system is consistant q using matrix ? X2 - 4X3 2X1 -3X2 +2X3 =l 5x,…

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Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

A:

Q: 13. Using the transformation matrix, the result of mirroring the rectangle (0,0), (2,0), (2,2),…

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Q: 4. Consider the matrix 1 0 0 0 0 0 -2a -a (a² + a) 0 (2-a²) - (2-a²) -2a (2-a²) 2+ 4a - a² Find all…

A: 4) Solution:According to the given data, find the all values of a for which given matrix is psd.

Q: Table Q4(b) is generated from the function f(x)=e* – 4x² + B , where B is the last two digits of…

A: here question has a mistake , though I correct it and solve it for you, here two different f(x) is…

Q: Find the standard matrix for the linear transformation T. T(x₁, x₂) = (0, 0) ↓↑

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Q: Let T,(x1,x2) = (+4x1 – 5z2, +1æ1 – lz2), and T2(x1,X2) = (- 321 – 5æ2 , +5æı + 8x2). Write the…

A: To find the standard matrices for T1,T2 and T10T2.

Q: 6. Find the matrix of the quadratic form. Assume x is in R³. a. 3x} – 2x3 + 5.x + 4x1x2 – 6x1X3 b.…

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Q: Prove that translation of an n-dimensional point by multiplication by an n × n matrix is not a…

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Q: Find a matrix that implements the linear transformation T(x1,x2) = (3x1-4X2, X1-X2, 2x1 + x2)

A: A linear transformation is a function satisfying the following properties: where x and y are…

Q: 3. Let B = {[4] [7]} and c={[7][7]} 4 9 C a. Find the change of coordinate matrix from C to B.

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Q: The linear transformation 2x y T 3z+w X - w is written as a matrix multiplication T : A What is the…

A: The linear transformation,Txyzw=2x3z+wx-w

Q: What is the standard matrix for the linear transformation given by a clockwise rotation by 45°…

A: We will first find Reflection matrix and then rotation   Later as per requirement, we will find…

Q: 3. Let A, B € Mnxn (F) be n x n matrices. (a) Prove that tr(A + B) = tr(A) + tr(B). (b) Prove that…

A: Trace of matrices is sum of its  diagonal entries

Q: Let A = (a) and B = (A + B)(A + B) (b) A2 + 2AB + B² 3) Let A2 and B2 denote the matrix products AA…

A: A=5423B=8759

Q: Find the transformation matrix for the following figure: B'(-5,3) A(-5,0) C(-3,0) B(-5,-3) A(-3,-3)

A: Given the triangle A(−3,−3),B(−5,−3),C(−3,−6).We need to find the transformation matrix so that we…

Q: Consider the LP problem: Maximize 3xı + 2x2 subject to: x1 – x2 + 2x3 9 3x1 + x2 – x3 0 Find the…

A: Given LP problem is, x1-x2+2x3≤82x1+x2-x3≥6x1+3x2≥93x1+x2-x3≤10x1,x2,x3≥0 The canonical form of LP…

Q: 6 -1 Evaluate ABT – 3C given that (2 -2 lo -1 2. -2 A = 6 -3 ‚B = and C = -12 7. 3. Use matrix…

A: To solve the given matrix problems.

Q: 8 Consider a square matrix B whose inverse is given by B'. a In terms of B", what is the inverse of…

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Q: 2. Determine whether the matrix transformation T(x,y)=(3x,-5.x) is one- to-one.

A: T is not one-to-one.Explanation:

Q: ind the 3x3 matrix that is equivalent in it's action to each of the

A: Given: To find 3×3 matrix that  equivalent to the symmetry operators are, a  S^2zb  C^2z

Q: For the​ matrixA=daig(-2,-1,2), put the following values in increasing​ order: det(A),​ rank(A),…

A: Given the matrix A=daig(-2,-1,2) is diagonal matrix Therefore the eigen values of A are -2, -1, 2.

Q: Write f= x + 10x1x2 + x3 as a difference of squares, and f= x? + 10x,x2 + 30x as a sum of squares.…

A: Given f=x12+10x1x2+x22.  Let the associated matrix of f be A=abba is 2×2 symmetric matrix. Then,…

Q: [102] 6. Find the kernel of the linear transformation whose standard matrix is B= 215. [237]

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Q: (a) Show that the jth column of the matrix product AB is equal to the matrix product Ab;, where b;…

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Q: diag(a1, ..., an) be a diagonal matrix (i.e., the matrix with the numbers a1, ..., an on the main…

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Q: Find the matrix A of the linear transformation from R² to R³ given by T([2]) = 4-88 A = 91 +5

A: Given:- Tx1x2=693x1+-75-6x2

Q: For each of the following, factor the matrix A into a product QDQ' where Q is orthogonal and D is…

A: A is symmetric matrix ,then A is orthogonally diagonalizable, and Q is the orthogonal matrix, the…

Q: and (96) = C1 A₁-3+4i with ₁ = Write the solution to the linear system [+] in the following forms.…

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Q: 10. 10a. Let T be an injective linear transformation from R to R. Let A be the matrix associated to…

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Q: a) Let A and B be two regular (nonsingular) (n, n)-matrices. Determine whether the following is…

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Q: For the matrixA=daig(-2,-1,2), put the following values in increasing order: det(A), rank(A),…

A: The given matrix is,  A = diag(-2, -1, 2). We have to put the following quantities in increasing…

Q: - Create a table that counts from 0-100 in intervals of 18. - Look at the tensor below 29 0 -51] G 0…

A: Since, you have posted multiple questions but according to guidelines we will solve first question…

Q: Consider the matrix A = show that the product L(X)=Ai is a linear transformation, where žER*.

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Q: Show your work. Simplify your results. -{()}--0). and b=0 2 Let L = Span (a) (b) (c) Find the matrix…

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Q: in

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Q: b) Evaluate det[(2A)-1 (3A")], where A is any invertible (2 x 2) matrix.

A: