Let A be an (n × n) matrix. We apply the elementary transformation of type 1 to A: "add m times row j to row i" (i.e. row i + mx row j), where m is a non-zero constant and j < i. a) Show that this transformation is encoded as a matrix multiplication L · A where L has the following form: 1 1 m 1 1 where m is in the entry (i, j). b) Write down a closed form for the matrix L-'. Multiplying with L-1 from the left also corresponds to an elementary transformation of type 1, what is this transformation?

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A: Given, Let A be an n×n matrix and suppose that L:Mnn→Mnn is defined by L(x)=AX, for all X∈Mnn

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A: Matrix

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A: Introduction: A transformation matrix is a matrix that, through matrix multiplication, transforms…

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A: In this problem we used Gram-Schmidt orthogonalization  process.

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A: please see the next step for solution

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Q: Find a matrix A that induces the transformation TRR given below. [-5x+3y] 10x-Sy 0 00 A=0 00 0 0 0

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Q: let  A and  B be  square  matrices of order n  such that  Ax=Bx  and x belongs to Rn  then   find…

A: Ax = Bx implies  Ax - Bx = O So, (A - B)x = O where x belongs to Rn  So, x belongs to the null space…

Q: 1: Let A= be the standard matrix representing the linear transformation L. ind L |Find L

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Q: Let A be the n × n matrix given by Show that det (A) = (a - 1) n − 1(a + n - 1)

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Q: given below. Find a matrix A that induces the transformation T:R→R- -4x+7y+8z -2x+10y+3z Ty

A: The transformation T:ℝ3→ℝ2Txyz=-4x+7y+8z-2x+10y+3z