6. Consider the bases B = {P₁, P₂} and B' = {₁,₂} for P₁, where P₁ = 6 + 3x, P₂ = 10 + 2x, q₁ = 2, q₂ = 3 + 2x a. Find t
Posted: Mon Jul 11, 2022 12:44 pm
- 6 Consider The Bases B P P And B For P Where P 6 3x P 10 2x Q 2 Q 3 2x A Find T 1 (30.67 KiB) Viewed 32 times
- 6 Consider The Bases B P P And B For P Where P 6 3x P 10 2x Q 2 Q 3 2x A Find T 2 (39.11 KiB) Viewed 32 times
6. Consider the bases B = {P₁, P₂} and B' = {₁,₂} for P₁, where P₁ = 6 + 3x, P₂ = 10 + 2x, q₁ = 2, q₂ = 3 + 2x a. Find the transition matrix from B' to B. b. Find the transition matrix from B to B'. c. Compute the coordinate vector [p]B, where p = −4+ x, and use (11) to compute [p]B¹. d. Check your work by computing [p], directly.
8. Let S be the standard basis for R², and let B = {V₁, V₂} be the basis in which v₁ = (2, 1) and v₂ = (−3, 4). a. Find the transition matrix PB-s by inspection. b. Use Formula (14) to find the transition matrix PS-B- c. Confirm that PB→s and Ps→B are inverses of one another. d. Let w = (5,-3). Find [w] and then use Formula (12) to compute [w]s. e. Let w = (3,-5). Find [w]s and then use Formula (11) to compute [w]B.