Consider a transformation T: R3 → R2 where R3 and R2 represent three and two-dimensional real column vectors respectively. Also, T(x) = Ax for some matrix A and for each x in R3. How many rows and columns do A have and what is it's maximum possible rank?

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TuteeHUB · Accepted Answer

Rows : 2; Columns : 3; Rank : 3

TuteeHUB · Answer

Rows: 3; Columns : 2; Rank : 3

TuteeHUB · Answer

Rows : 3; Columns : 2; Rank : 2

TuteeHUB · Answer

Rows : 2; Columns : 3; Rank : 2

1.	Consider a transformation T: R3 → R2 where R3 and R2 represent three and two-dimensional real column vectors respectively. Also, T(x) = Ax for some matrix A and for each x in R3. How many rows and columns do A have and what is it's maximum possible rank?
A.	Rows: 3; Columns : 2; Rank : 3
B.	Rows : 3; Columns : 2; Rank : 2
C.	Rows : 2; Columns : 3; Rank : 2
D.	Rows : 2; Columns : 3; Rank : 3
Answer» D. Rows : 2; Columns : 3; Rank : 3

Consider a transformation T: R3 → R2 where R3 and R2 represent three and two-dimensional real column vectors respectively. Also, T(x) = Ax for some matrix A and for each x in R3. How many rows and columns do A have and what is it's maximum possible rank?

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