SOLUTION: Let 𝐴 be a 𝑎×𝑏 matrix. If the linear transformation 𝑇(𝑥) from ℝ3 to ℝ6 is defined by 𝑇(𝑥)=𝐴𝑥, how many rows and columns does the matrix 𝐴 have?

Question 1192014: Let 𝐴 be a 𝑎×𝑏 matrix. If the linear transformation 𝑇(𝑥) from ℝ3 to ℝ6 is defined by 𝑇(𝑥)=𝐴𝑥, how many rows and columns does the matrix 𝐴 have?
𝑎=?, 𝑏= ?
Answer by ikleyn(52848) (Show Source): You can put this solution on YOUR website!
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Then a= 6, b= 3.    ANSWER



The input vector "x" has 3 component; therefore, matrix "A" should have 3 columns to act on the three components of "x" :  b = 3.


The output vector T(x) has 6 component; therefore, matrix A has 6 rows to provide 6 components of the output vector T(x):  a = 6.

Solved and explained.

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