For the following transformation T either give its standard matrix (i.e. the mat
ID: 2938725 • Letter: F
Question
For the following transformation T either- give its standard matrix (i.e. the matrix relative to thestandard bases of the domain of T and the codomain of T), if T islinear, or
T æ
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ç
ç
ç
ç
è é
ê
ê
ê
ê
ê
ë x1 x2 x3 x4 ù
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ú
ú
ú
ú
û ö
÷
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÷
÷
÷
ø = é
ê
ê
ê
ë 6 x1-x2+x3 5 x1-2 x2-4 x3-3 x4 3 x1-4 x2+6 x3-3 x4+6 ù
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û Enter your answer as follows. Take care to read theseinstructions; the usual type/syntax checking is not possible with"matrix" entries. So type/syntax errors will attractpenalties.
- If T is linear enter the entries ofits standard matrix starting at the cell in the top lefthandcorner, and leave any cells you don't needempty.
- Similarly, to enter a counter-example of L2enter a scalar k and three vectors
k v T(kv) k T(v) in that order in the 4 cells of the top row of thetable, leaving all other cells empty. To be acounter-example of L2, you musthave
T(k v) ¹ k T(v) Shorthand notation for vectors. Usethe following shorthand to enter your vectors:separate the entries by commas and enclose inc( ), e.g. c(1, 2 ,3) representsthe column vector
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ë 1 2 3 ù
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û
Answer: Enter your answer as follows. Take care to read theseinstructions; the usual type/syntax checking is not possible with"matrix" entries. So type/syntax errors will attractpenalties.
- If T is linear enter the entries ofits standard matrix starting at the cell in the top lefthandcorner, and leave any cells you don't needempty.
- Similarly, to enter a counter-example of L2enter a scalar k and three vectors
k v T(kv) k T(v) in that order in the 4 cells of the top row of thetable, leaving all other cells empty. To be acounter-example of L2, you musthave
T(k v) ¹ k T(v) Shorthand notation for vectors. Usethe following shorthand to enter your vectors:separate the entries by commas and enclose inc( ), e.g. c(1, 2 ,3) representsthe column vector
é
ê
ê
ê
ë 1 2 3 ù
ú
ú
ú
û
ç
ç
ç
ç
ç
è é
ê
ê
ê
ê
ê
ë x1 x2 x3 x4 ù
ú
ú
ú
ú
ú
û ö
÷
÷
÷
÷
÷
ø = é
ê
ê
ê
ë 6 x1-x2+x3 5 x1-2 x2-4 x3-3 x4 3 x1-4 x2+6 x3-3 x4+6 ù
ú
ú
ú
û
Explanation / Answer
Enter your answer as follows. Take care to read theseinstructions; the usual type/syntax checking is not possible with"matrix" entries. So type/syntax errors will attractpenalties.- If T is linear enter the entries ofits standard matrix starting at the cell in the top lefthandcorner, and leave any cells you don't needempty.
- Similarly, to enter a counter-example of L2enter a scalar k and three vectors
k v T(kv) k T(v) in that order in the 4 cells of the top row of thetable, leaving all other cells empty. To be acounter-example of L2, you musthave
T(k v)¹ k T(v) Shorthand notation for vectors. Usethe following shorthand to enter your vectors:separate the entries by commas and enclose inc( ), e.g. c(1, 2 ,3) representsthe column vector
é
ê
ê
ê
ë 1 2 3 ù
ú
ú
ú
û
ç
ç
ç
ç
ç
è é
ê
ê
ê
ê
ê
ë x1 x2 x3 x4 ù
ú
ú
ú
ú
ú
û ö
÷
÷
÷
÷
÷
ø = é
ê
ê
ê
ë 6 x1-x2+x3 5 x1-2 x2-4 x3-3 x4 3 x1-4 x2+6 x3-3 x4+6 ù
ú
ú
ú
û