1. For the following linear transformation, T, malo nins W1 = 3x1- 6xX2+ 2x3 w2 = -2x1 + 4x2 + x3 W3 = X1-2x2-x3 W4 =-X1+ 2x2 + 2x3 | %3D i) Find the matrix that represents this transformation. ii) Determine the domain of T. o nielox Somo T (vix iii) Determine the codomain ofT.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
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Chapter2: Second-order Linear Odes
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1. For the following linear transformation, T,
n niamalo ni d
W1 = 3x1-6x2 + 2x3
W2 = -2x1 + 4x2 + x3
W3 = X1 - 2x2- X3
W4 = -X1 + 2x2 + 2x3
ba G
Find the matrix that represents this transformation.
ii)
Determine the domain of T.
nielqx Somo T 4 (vix
iii)
Determine the codomain of T.
iv)
Find a basis for ker(T).
I to lamsd ohot aiesd e bniu
v)
Determine the dimension of the ker(T).
vi)
Find a basis for range(T).
anincesn oy mieiqx Sono-ot-ono T z
vii)
Determine the dimension of the range(T).
ximem ssvni s ariy uuoC).noismolan
TAMSO12AST
viii)
Is T a one-to-one mapping? Explain your reasoning.
ix)
Is T an onto mapping? Explain your reasoning.
Determine whether the linear transformation defined by the equations is
invertible; if so, find the standard matrix for the inverse transformation, and find
T. If it is not invertible, explain why.
x)
Transcribed Image Text:1. For the following linear transformation, T, n niamalo ni d W1 = 3x1-6x2 + 2x3 W2 = -2x1 + 4x2 + x3 W3 = X1 - 2x2- X3 W4 = -X1 + 2x2 + 2x3 ba G Find the matrix that represents this transformation. ii) Determine the domain of T. nielqx Somo T 4 (vix iii) Determine the codomain of T. iv) Find a basis for ker(T). I to lamsd ohot aiesd e bniu v) Determine the dimension of the ker(T). vi) Find a basis for range(T). anincesn oy mieiqx Sono-ot-ono T z vii) Determine the dimension of the range(T). ximem ssvni s ariy uuoC).noismolan TAMSO12AST viii) Is T a one-to-one mapping? Explain your reasoning. ix) Is T an onto mapping? Explain your reasoning. Determine whether the linear transformation defined by the equations is invertible; if so, find the standard matrix for the inverse transformation, and find T. If it is not invertible, explain why. x)
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