Please answer d, e, f 9:07 PM Tue Dec 117% IT.+: 0The theorems about determinants and areas/volumesof parallelepipeds always consider "full-dimensional"shapes, like 2-dimensional shapes in R², 3-dimensional shapes in R³, and n-dimensional shapesin R". Let's see what happens when we consider alower-dimensional shape in a bigger-dimensionalspace.(a) Let T be the linear transformation from R3 to R3given by orthogonal projection onto the xy-plane.(Then T is represented by the matrix1 0 00 1 0.) What is det A?A =(b) Let N be the 2-dimensional square in R3 definedГоbyand(which lies in the xy-plane). Whatis the area of N?1What is thearea of T(N)?(c) Now let B be the transformation of R3 defined by[10 2 00 03(d) What is det B? 6(e) Let N be the same parallelogram as in part (b). What isthe area of the transformed parallelogram B(N)?6Is the ratio Area(B(N))/Area(2)equal to | det B|? (Write "yes" or "no". Capitalization doesn'tmatter.) yes.So, in summary, let's think more generally:(f) True/false. If N is a 2-dimensional parallelogram inside R3and T(a) = A is a linear transformation from R3 to R³,then the area of T(N) is equal to | det A| · (area of N).(Write "true" or "false". Capitalization doesn't matter)

Name: Please answer d, e, f 9:07 PM Tue Dec 117% IT.+: 0The theorems about d
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: Please answer d, e, f 9:07 PM Tue Dec 117% IT.+: 0The theorems about determinants and areas/volumesof parallelepipeds always consider "full-dimensional"shapes, like 2-dimensional shapes in R², 3-dimensional shapes in R³, and n-dimensional shapesin R"