Solution Found!
Let the linear map T : R2 R2 have standard matrix A = 2 1 1 2 _ . a. Calculate the
Chapter 4, Problem 27(choose chapter or problem)
Let the linear map T : R2 R2 have standard matrix A = 2 1 1 2 _ . a. Calculate the matrix for T with respect to the basis B = # 1 2 1 1 _ , 1 2 1 1 _$ . b. Set y = CB(x), and calculate Ax x = 2x2 1 2x1x2 + 2x2 2 in terms of y1 and y2. c. Use the result of part b to sketch the conic section 2x2 1 2x1x2 + 2x2 2 = 3. (See also Section 4.1 of Chapter 6.)
Questions & Answers
QUESTION:
Let the linear map T : R2 R2 have standard matrix A = 2 1 1 2 _ . a. Calculate the matrix for T with respect to the basis B = # 1 2 1 1 _ , 1 2 1 1 _$ . b. Set y = CB(x), and calculate Ax x = 2x2 1 2x1x2 + 2x2 2 in terms of y1 and y2. c. Use the result of part b to sketch the conic section 2x2 1 2x1x2 + 2x2 2 = 3. (See also Section 4.1 of Chapter 6.)
ANSWER:Step 1 of 5
a. Use the basis to determine the matrix for
It is known that the standard matrix for is .
Let and .
Find the image of under and write it as a linear combination of and .
So,