Assume that T is a linear transformation. Find the standard matrix of T. T

Isa Trevino

Isa Trevino

Answered question

2021-09-28

T must be a linear transformation, we assume. Identify the T standard matrix. ๐Ÿš๐ŸšT:R2โ†’R2 is a vertical shear transformation that maps e1 into e1โˆ’2e2 but leaves the vector e2 unchanged.

Answer & Explanation

stuth1

stuth1

Skilled2021-09-29Added 97 answers

T(e1)=e1โˆ’2e2andT(e2)=e2 Here, e1ย andย e2 are the unit vectors, as you can see in the next step
T(e1)=[10]โˆ’2[01]=[1โˆ’2]ย andย T(e2)=[01] Writing the above as a matrix yields these equation
T=[10โˆ’21] According to theorem 10, the transformation matrix equals the transformation of the unit vectors, each occupying one column in this matrix.
Result:
T=[10โˆ’21]

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