Finding Standard Matrices for Compositions In Exercises 47 and 48, find the standard matrices for T = T 2 T 1 and T ′ = T 1 T 2 . T 1 : R 2 → R 3 , T 1 ( x , y ) = ( x , x + y , y ) T 2 : R 3 → R 2 , T 2 ( x , y , z ) = ( 0 , y )
Finding Standard Matrices for Compositions In Exercises 47 and 48, find the standard matrices for T = T 2 T 1 and T ′ = T 1 T 2 . T 1 : R 2 → R 3 , T 1 ( x , y ) = ( x , x + y , y ) T 2 : R 3 → R 2 , T 2 ( x , y , z ) = ( 0 , y )
Solution Summary: The author explains that the standard matrices for T=T_1 and tprime are left[cc0
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Solve the linear system of equations attached using Gaussian elimination (not Gauss-Jordan) and back subsitution.
Remember that:
A matrix is in row echelon form if
Any row that consists only of zeros is at the bottom of the matrix.
The first non-zero entry in each other row is 1. This entry is called aleading 1.
The leading 1 of each row, after the first row, lies to the right of the leading 1 of the previous row.
Chapter 6 Solutions
Bundle: Elementary Linear Algebra, Loose-leaf Version, 8th + WebAssign Printed Access Card for Larson's Elementary Linear Algebra, 8th Edition, Single-Term
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