Lines and planes
... Its entries vi are called the components of ~v . Similarly a row vector is a matrix consisting of a single row. In what follows the word vector always means column vector. We think of the vector ...
... Its entries vi are called the components of ~v . Similarly a row vector is a matrix consisting of a single row. In what follows the word vector always means column vector. We think of the vector ...
![M.E. 530.646 Problem Set 1 [REV 1] Rigid Body Transformations](http://s1.studyres.com/store/data/017245963_1-2f60978169e1255dbeaf6de62def96e1-300x300.png)
M.E. 530.646 Problem Set 1 [REV 1] Rigid Body Transformations
... the multiplication of a polynomial by a scalar. For example, let x1 = s2 + 3s + 1, and x2 = s5 , then x1 + x2 = s5 + s2 + 3s + 1. b. Show that xi = si−1 , i = 1, . . . , n form a basis for the LVS. (Hint: show linear independence by making an argument about the expression p0 + p1 s1 + · · · pn−1 sn ...
... the multiplication of a polynomial by a scalar. For example, let x1 = s2 + 3s + 1, and x2 = s5 , then x1 + x2 = s5 + s2 + 3s + 1. b. Show that xi = si−1 , i = 1, . . . , n form a basis for the LVS. (Hint: show linear independence by making an argument about the expression p0 + p1 s1 + · · · pn−1 sn ...
LINEAR ALGEBRA (1) True or False? (No explanation required
... Explanations: matrices like ( 10 00 ) or ( 11 11 ) are nonzero but do not have an inverse. Matrices have an inverse if and only if they are nonsingular square matrices. If A and B are nonsingular, then so is AB, and its inverse clearly is B −1 A−1 since B −1 A−1 AB = B −1 IB = B −1 B = I. In general ...
... Explanations: matrices like ( 10 00 ) or ( 11 11 ) are nonzero but do not have an inverse. Matrices have an inverse if and only if they are nonsingular square matrices. If A and B are nonsingular, then so is AB, and its inverse clearly is B −1 A−1 since B −1 A−1 AB = B −1 IB = B −1 B = I. In general ...
