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*2. A matrix maps a point P to a point Q if it maps the position vector of P to the position vector of Q. To figure out
Posted: Thu Jul 14, 2022 4:03 pm
by answerhappygod
- 2 A Matrix Maps A Point P To A Point Q If It Maps The Position Vector Of P To The Position Vector Of Q To Figure Out 1 (119.66 KiB) Viewed 37 times
*2. A matrix maps a point P to a point Q if it maps the position vector of P to the position vector of Q. To figure out where a matrix sends a set of points, we apply the matrix to every single point in our set and then put all the resulting points together. (a) Consider the matrix and vectors A=⎝⎛1−10234324⎠⎞,p=⎝⎛201⎠⎞,d=⎝⎛1−23⎠⎞ and let line ℓ be the set of all points (x,y,z) such that ⎝⎛xyz⎠⎞=p+td for some real value of t. Prove that A sends line ℓ to another line and figure out the direction vector for this line. (b) Find a vector p1 and a non-zero vector d1 such that the matrix A above sends the line parametrized as ⎝⎛xyz⎠⎞=p1+td1 to a single point.