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Consider the two linear functions h: R3 P2 and 9: P2 → M2x2 given as here. a b → (a+b)x² + (2a + 2b)x + c px²+qx+r › C² P P-2q C Use these bases for the spaces. B = | C=(1+x,1x,x²) D= " " 3 " (a) Give the formula composition map go f: R³ → M2x2 directly from the above definition. (b) Represent ƒ and g with respect to the appropriate bases. (c) Represent gf with resepct to the appropriate bases. (d) Check that the two matrices from the second part multiply to the matrix from the third part.

Consider the two linear functions h: R3 P2 and 9: P2 → M2x2 given as here. a b → (a+b)x² + (2a + 2b)x + c px²+qx+r › C² P P-2q C Use these bases for the spaces. B = | C=(1+x,1x,x²) D= " " 3 " (a) Give the formula composition map go f: R³ → M2x2 directly from the above definition. (b) Represent ƒ and g with respect to the appropriate bases. (c) Represent gf with resepct to the appropriate bases. (d) Check that the two matrices from the second part multiply to the matrix from the third part.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the two linear functions h: R3 P2 and 9: P2 → M2x2 given as here. a b → (a+b)x² + (2a + 2b)x + c px²+qx+r › C² P P-2q C Use these bases for the spaces. B = | C=(1+x,1x,x²) D= " " 3 " (a) Give the formula composition map go f: R³ → M2x2 directly from the above definition. (b) Represent ƒ and g with respect to the appropriate bases. (c) Represent gf with resepct to the appropriate bases. (d) Check that the two matrices from the second part multiply to the matrix from the third part.
Transcribed Image Text:Consider the two linear functions h: R3 P2 and 9: P2 → M2x2 given as here. a b → (a+b)x² + (2a + 2b)x + c px²+qx+r › C² P P-2q C Use these bases for the spaces. B = | C=(1+x,1x,x²) D= " " 3 " (a) Give the formula composition map go f: R³ → M2x2 directly from the above definition. (b) Represent ƒ and g with respect to the appropriate bases. (c) Represent gf with resepct to the appropriate bases. (d) Check that the two matrices from the second part multiply to the matrix from the third part.
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