<p>Find the standard matrix of the linear transformation
T: R2 -> R3 defined by
T( <1,0> ) = e2+e3,
T( <0,1> ) = e1-e3</p>
<p>is this a hw problem or from section or what?</p>
<p>Yes, it is one of the homework problems from section 01 of Math 54. Wondering if anyone can figure it out.</p>
<p>your username reminds me of a song line</p>
<p>“My GPA is 4.0,
How to party I don’t know…”</p>
<p>^ Math is way more fun than any party at Berkeley. I’ll be laughing at all you losers with anything less than a 4.0 ;D</p>
<p>what chapter/# is it?</p>
<p>I have a 4.0 but don’t take this things too personally</p>
<p>(and no, math isn’t as fun as partying for me, but to each his own :D)</p>
<p>If T: V –> W is a linear map on vector spaces, and v<em>1,…,v</em>n a basis for V, w<em>1,…,w</em>m one for W, then the general form for the matrix with respect to these bases has ith column consisting of coordinates of Tv<em>i with respect to the w</em>j (this means write Tv<em>i as a linear combination of the w</em>j and form the coordinate matrix given by these coefficients). In your case, v<em>i are the (1,0) and (0,1) and the w</em>j are the e_j, which presumably are the standard basis vectors for R^3. </p>
<p>I’d assume the standard matrix, then, is the matrix written with respect to the standard bases, which is what it appears the data given tell you how to do.</p>
<p>The matrix of a linear transformation may be found by assembling the images of the standard basis vectors under the transformation into a matrix. Since they give you those images, T(<1,0>) = <0,1,1> and T(<0,1>) = <1,0,-1>, the matrix will be:
[0,1]
[1,0]
[1,-1]</p>