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thanks Although it seems silly, it is possible to do elementary row operations o

ID: 2969035 • Letter: T

Question

thanks

Although it seems silly, it is possible to do elementary row operations on n x 1 matrices. Every such operation defines a transformation of Rn into Rn. For example, if we define a transformation of R3 into R3 by "add twice row 1 to row 3," this transformation transforms Since this transformation is described by a matrix, we see that our elementary row operation defines a linear transformation. A transformation defined by a single elementary row operation in called an elementary transformation and the matrix that describes such a transformation is called an elementary matrix. Find matrices that describe the following elementary row operations on Rn for the given value of n. Add twice row 3 to row 2 in R4. Multiply row 2 by 17 in R3. Interchange rows 1 and 2 in R4.

Explanation / Answer

1) Solution:

R^4 = [ 1 0 0 0]

[ 0 1 0 0]

[ 0 0 1 0]

[ 0 0 0 1]


a) we do operation : R2 + 3(R3) =

[ 1 0 0 0]

[ 0 1 3 0]

[ 0 0 1 0]

[ 0 0 0 1]


c) We interchange R1 <-> R2

[ 0 1 0 0]

[ 1 0 0 0]

[ 0 0 1 0]

[ 0 0 0 1]



2)

R^3 = [ 1 0 0]

[ 0 1 0]

[ 0 0 1]


R2 --> 17 (R2)

[ 1 0 0]

[ 0 17 0]

[ 0 0 1]



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