- #1

HF08

- 39

- 0

...[sin[tex]\theta[/tex] cos[tex]\theta[/tex]]

for some [tex]\theta[/tex] in R[tex]^{2}[/tex].

(a) Prove that || B

*(x,y)*|| = ||

*(x,y)*|| for all

*(x,y)*[tex]\in[/tex]R[tex]^{2}[/tex]

Question: What does B(x,y) and (x,y) notation mean?

I have a result that says

Let B=[b[tex]_{ij}[/tex]] be an mxn matrix whose entries

are real numbers and let

**e[tex]_{1}[/tex]**,...,

**e[tex]_{n}[/tex]**represent the usual basis of

**R^n**. If T(

**x**) = B

**x**,

**x**[tex]\in[/tex]

**R^n**, then T is a linear function from

**R^n**to

**R^m**and T(

**e[tex]_{j}[/tex]**)=(b[tex]_{1j}[/tex],b[tex]_{2j}[/tex],...,b[tex]_{mj}[/tex], j = 1,2,...n

Warning: Superscripts are not superscipts. They are supposed to be SUBSCRIPTS. Sigh.

Can I use this?

1. I am very new to this material

2. I am stuck with the notation.

3. Please answer my first question carefully. I can't answer the question unless I know what they are asking. :)

Please help me. Thank You,

HF08