MATH 1104 Lecture Notes - Lecture 16: Linear Map

• School: Carleton University
• Department: Mathematics
• Course: MATH 1104
• Professor: Mohammad Sadeghi

Document Summary

5. 3 standard matrix for linear transformation: find standard matrix for linear transformation for t: rn to rm, the standard matrix is m x n, denoted as a(t), t (inxn) = a(t), Example the standard matrix a(t) is 2 x 3. the value into the right half to form the first column of the standard matrix. T is a linear transformation from r3 to r2, given as (cid:1876)(cid:1877)(cid:1878) = (cid:1876)+(cid:1877) (cid:1878) (cid:884)(cid:1876) , T (cid:883) (cid:882) (cid:882) (cid:882) (cid:883) (cid:882) (cid:882) (cid:882) (cid:883) = a(t). For the first column, take the standard basis for r3 (cid:1876)(cid:1877)(cid:1878) = (cid:883)(cid:882)(cid:882) , meaning x = 1, y = 0, z = 0, plug (cid:882) (cid:884) (cid:883) = (cid:883) (cid:884) , taking (cid:1876)(cid:1877)(cid:1878) = (cid:883)(cid:882)(cid:882) C1 = (cid:1876)+(cid:1877) (cid:883)+(cid:882) (cid:1878) (cid:884)(cid:1876) = (cid:882) (cid:884) (cid:882) = (cid:883)(cid:882) , taking (cid:1876)(cid:1877)(cid:1878) = (cid:882)(cid:883)(cid:882) C2 = (cid:1876)+(cid:1877) (cid:1878) (cid:884)(cid:1876) = (cid:882)+(cid:883) (cid:883) (cid:884) (cid:882) = (cid:882)(cid:883), taking (cid:1876)(cid:1877)(cid:1878) = (cid:882)(cid:882)(cid:883)