For the following transformation T either give its standard matrix (i.e. the mat
ID: 2938695 • 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 ?
ç
ç
ç
è é
ê
ê
ê
ë x y z ù
?
?
?
û ?
÷
÷
÷
? = é
ê
ê
ë 6 x-y+5 z -6 x-y+z+2 ù
?
?
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
é
ê
ê
ê
ë 1 2 3 ù
?
?
?
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
?
?
?
û
ç
ç
ç
è é
ê
ê
ê
ë x y z ù
?
?
?
û ?
÷
÷
÷
? = é
ê
ê
ë 6 x-y+5 z -6 x-y+z+2 ù
?
?
û