(4) Let B be the matrix 1 1 3 B = 2 3 4 -1 -3 1 -6 -2 and let TB : Rª → R³ be the linear transformation TB(x) = Bx. (4a) Is TB one-to-one? How do we know?

Q: 1. Calculate exp(A) where A is the 2×2 matrix given by A 7 -2 -[33] = 5 5

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Q: Find the standard matrix of the given linear transformation from R2 to R². Projection onto the line…

A: The linear transformation from ℝ2 to ℝ2 is a projection onto the line y=-x. We have to find the…

Q: Let S be a linear transformation from R³ to R2 with associated matrix Let T be a linear…

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Q: - 4 V, = X2 and v2= 7 and let T: R2-→R? be a linear transformation that maps x into x,v, + X,V2.…

A: That's easy. Have a great day!!!

Q: Find the matrix M of the linear transformation T : R3 → R2 given by () [ = M: T -9x1 + x2 + (-4)x3…

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Q: Consider a linear transformation T from R³ to R2 Find the matrix A of T. A = for which CD-· -· D-4 0

A: Here for the given transformation we have to find the matrix A of T.

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: Determine a matrix A that describes the following linear transformation. T([*]) = [2x+³] 3y

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Q: Find a matrix corresponding to the linear transformation that rotates R clockwise by 45 degrees…

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Q: Let S be a linear transformation from R³ to R2 with associated matrix Let T be a linear…

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Q: Consider a linear transformation T from R³ to R² for which T ¹ (C) - · ~ (C) -· ¹(E) -- T = T 0 Find…

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

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Q: 3. If T(x) = Ax+b is a linear transformation where A is an mxn matrix and x is an n dimensional…

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Q: Derive the matrix that performs the following consecutive transformations (in augmented form): 1-…

A: (1) Let T be a transformation that translate 2- unit along x-axis. Therefore: Txyz=x+2yz Therefore…

Q: The matrix that projects onto the line y = 1 2 8 is X 0.6 0.8 0.8 -0.6

A: Let  be projection on the line Then  is  a linear transformation with matrix

Q: What matrix M performs the transformation sending A to A', B to B', C to C", and D to D'? В C A = A'…

A: We need the points A0,0, B0,1, C1,1, and D1,0 to be transformed to A'0,0, B'0,-12, C'2,-12, and…

Q: 2. Find the coordinate matrix of 7 = ³- {)-(-9)} B = 2 0 0 6 2 relative to the basis

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Q: Find the B-matrix for the transformation xAx, where B = {b₁,b₂}. -5 -1 2 A = [*] -0 -0 b₁ = b₂ 5 The…

A: Given that the matrices  A=-5-15-1  , b1=-1-1  , b2=21   .

Q: find the standard matrix for the reflection of IR squared about the line that makes an angle of π/4…

A: Consider line that makes an angle of  with positive  axis.To illustrate the standard matrix for…

Q: + 7 ((x²2₂) = [(²³ x 1 + x ²2₂] (ii) Find the matrix representation of T relative to the standard…

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Q: Let and B = A = 6 Find the matrix C of the linear transformation T(x) = B(A(x)). %3D C =

A: To find the matrix C such that Tx=BAx Tx=BAx=BAx so we need to multiply the matrix B and A