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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?

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? Correct Answer Rows : 2; Columns : 3; Rank : 2

Order of R3 = 3 × 1

Order of R2 = 2 × 1

Given that:

T(x) = Ax where x ϵ R3

Let the order of A be: m × n

Since A and x matrices are multiplying, n = 3

From the above options m = 2

So order of A :  2 × 3

Rank of A = min(2, 3) = 2

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