Jawapan

  • Pengguna Brainly
2016-04-03T19:57:58+08:00

Ini Jawapan Diperakui

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Jawapan diperakui mengandungi maklumat yang boleh dipercayai dan diharapkan yang dijamin dipilih dengan teliti oleh sepasukan pakar. Brainly mempunyai berjuta-juta jawapan berkualiti tinggi, semuanya disederhanakan dengan teliti oleh ahli komuniti kami yang paling dipercayai, tetapi jawapan diperakui adalah terbaik di kalangan terbaik.
This is actually easy to do: 
You take T of the standard basis vectors and make the results the columns of a matrix A. (You must keep them in order- colm 1 must be T of the first basis vector, colm 2 the second, etc) 
That will be the matrix that represents this transformation (that is, T(v) will equal Av - meaning taking T of a vector gives the same result as multiplying v on the left by A). 

The standard basis vectors are (1,0) and (0,1) 
then: 
T(1,0) = ( -4,2,0,1) 
T(0,1) = (-9, -5, -3, 6) 

Now let the matrix A be the 4x2 matrix with column 1 being (-4,2,0,1) and column 2 being (-9, -5, -3, 6) 
(That is, A will have row 1 = [ -4 -9], row 2 will = [ 2 -5 ], etc.) 

You can check this by taking some vector v and calculating T(v) and then Av and seeing you get the same result. 
Also, if you let w be the vector (x1,x2) and calculate Aw you will see you get back the formula for the transformation. Note: this is how you find the transformation if you are only given it's matrix. 

(of course, with the T form you input the vector as a row and you get out the answer as a row vector whereas with Av you put it in as a column vector and it gives it the answer as a column but it's the same result)