Write the matrix corresponding to the following linear transformations. 2x1 – x2 – x3 Yı Y2 = 3x3 Y3 = x1 + x2 2 -1 -1 3 1 2 -1 -1 3 1 2 -1 -1' 1 3 1 O [2 -1 -1 3 1 1 1

Q: Let T be a linear transformation from R³ into R³. Find T-1 T(x1,x2₁x3)=(2x₁-X3, X₁ + X₂ X3, X2-3x3)…

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Q: translate the two-dimensional matrix [[1 2] [3 4]] to the origin along the x axis. I want to see how…

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Q: Find the matrix M of the linear transformation T: R³. →>>> R² given by X1 (J- = -3x1 - x2 + 9x3 2x1…

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Q: Find the inverse transformation of y1=2x1+x2+x3 , y2=x1+x2+2x3 , y3=x1-2x3

A: To find the inverse function of the given transformation we need to recall a property of matrices as…

Q: First question: Find the inverse and determinate of the matrix A = [??H] -1-3 1 3 60 1 0 1 ||

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Q: b. fixes the origin c. both of the above 13. A matrix representation of the linear transformation…

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Q: M = Find the matrix M of the linear transformation T: R³ → R² given by 3 X1 (E)- = X3 T -9x1 - x2 +…

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Q: R2 → R3 first performs a horizontal shear that transforms  and then reflects points through line x2…

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Q: Suppose T: M2 2¬P2 is a linear transformation whose action on a basis for M22 is as follows: -1 0 3…

A: The detailed solution is as follows below:

Q: Is b in the range of the linear transformation X-Ax? Why or why not? A = 2 -4 1 -6 7 5 3-1 b -1 6

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Q: Study the kernel of the following linear transformations each what you now know about whether they…

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Q: (1 point) Find the inverse of the linear transformation 4x1 -1x2 %3D y2 -11x1 +3x2 %3D X1 = y2 » X2…

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Q: Suppose T : R² → R² is a linear transformation that first reflects points across the ₁-axis and then…

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Q: 25. Given that X and Y are two variables related by the equationY = aX² + bX,where a and b are…

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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: A= [2002], Now imagine you have a square (0,0), (1,0), (0,1) and (1,1). To what geometric object the…

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Q: Find the inverse transformation of y1=2x1+x2+x3 , y2=x1+x2+2x3  , y3=x1-2x3

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Q: Find the inverse of the linear transformation X1 = x2 = x3 = Y1+ Y₁+ Y1+ Y1 Y2 Y3 = = = 4x1 5x1 X1…

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Q: Find the standard matrix of the linear transformation. -131-1; -Y x + 2y 7x - 5y

A: As the linear transformation is from R2 to R3, the standard basis is (0, 1) and (1, 0) So, here…

Q: Suppose T: R² R² is a linear transformation that first reflects points across the ₁-axis and then…

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Q: A=(41] [4] ( )= (-1) [₂] + (3) [₂] 2

A: Matrix multiplication is possible if we have two matrices A and B such that, order of A =m×n;order…

Q: Find the inverse of the linear transformation Y1 Y2 Y3 = = = 2x₁ 2x₁ x1 +4x₂9x3 +3x₂ -7x3 +2x₂ - 4x3

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Q: iagonalize the following matrix: 21 4 1-4 31 -1 24001₁ 111-12 C - 0

A: A matrix is diagonalizable if A.m. of each eigen value = g.m. of corresponding eigen value

Q: A B -2 -2

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Q: The standard matrix of a linear transformation. 3 -1 [T] = -4 0

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Q: 2a + 56+c —а — 36 — 2с 3a + 76 +c -4a – 96 –c 2. T(а + bx + сх*). |

A: The objective is to write down the matrix of the given linear transformation withrespect to the…

Q: Which of the following transformations are linear? Y1 = -10x1 OA. Y2 = 6x1 Y3 = 3x1 OB. ( OC. Y2 Y3…

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