Let A= [a11 a12] [a21 a22) be a 2-by-2 matrix with extries from R. Define the determinanat of A, D(A), by the formula D(A)=a1la22- a12a21. a. Show that if A is the matrix of a distance preserving linear transformation T of R_2, then D(A)=+-1, and that D(A)=+1 if and only if A is a rotation, while D(A)=-1 if and only if A is a reflection.
Let A= [a11 a12] [a21 a22) be a 2-by-2 matrix with extries from R. Define the determinanat of A, D(A), by the formula D(A)=a1la22- a12a21. a. Show that if A is the matrix of a distance preserving linear transformation T of R_2, then D(A)=+-1, and that D(A)=+1 if and only if A is a rotation, while D(A)=-1 if and only if A is a reflection.
Chapter7: Systems Of Equations And Inequalities
Section7.8: Solving Systems With Cramer's Rule
Problem 3SE: Explain what it means in terms of an inverse for a matrix to have a 0 determinant.
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![Let A= [a11 a12]
[a21 a22]
be a 2-by-2 matrix with extries from R. Define the determinanat of A, D(A), by the formula D(A)=a1la22-
a12a21.
a. Show that if A is the matrix of a distance preserving linear transformation T of R_2, then D(A)=+-1, and
that D(A)=+1 if and only if A is a rotation, while D(A)=-1 if and only if A is a reflection.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6915687c-4f06-4661-ac02-aefc88931b4a%2F478f8a67-2ac7-48f2-971a-e2f32cdaf210%2F917a4z_processed.png&w=3840&q=75)
Transcribed Image Text:Let A= [a11 a12]
[a21 a22]
be a 2-by-2 matrix with extries from R. Define the determinanat of A, D(A), by the formula D(A)=a1la22-
a12a21.
a. Show that if A is the matrix of a distance preserving linear transformation T of R_2, then D(A)=+-1, and
that D(A)=+1 if and only if A is a rotation, while D(A)=-1 if and only if A is a reflection.
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