Please solve this Its linear algebra 1. If the statement is always true, circle

Question

Please solve this
Its linear algebra
1. If the statement is always true, circle True. If the statement is sometimes false, circle Faise. In each case, write a careful and clear justification or counterexample. (a) If A is a 2 × 3 matrix and T is a linear transformation True False defined by T(x) = Ax, then the domain of T is R2. 111 x 2X (b) A transformation T is linear if and only if Faise Telv, + cys) = c,T(v) + cZTv2) for all vi, v2 in the domain of T and all scalars c,c (c) The mapE-S:1 is a linear transformation. z| |z + yl transformation. True False

Explanation / Answer

Ans(1.a):
Your answer and reasoning is correct.

Ans(1.b):
Yes that is True as it is definition of linear transformation.

Ans(1.c):
Linear transformation is given by T(x)=Ax
then A must be a 2x2 matrix
[x+y]
[y ]
can be obtained using A=
[1   1]
[0   1]
but there is no option to manage -1 of y-1

so answer will be False.

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