![1.7 Lecture Notes (Part I) pdf]](http://s1.studyres.com/store/data/008845381_1-df4c9466ddca13fffa9818389c38ed17-300x300.png)
Sample Final Exam
... S = p(x) ∈ P3 p(2) − p(1) = 0 Find a basis for this subspace. Answer: Suppose that p(x) = ax2 + bx + c is a polynomial in S. Then, p(2) = 4a + 2b + c and p(1) = a + b + c, so that p(2) − p(1) = 3a + b. Thus, 3a + b = 0, so b = −3a. Thus, we can write p(x) as p(x) = ax2 − 3ax + c = a(x2 − 3x) + c Th ...
... S = p(x) ∈ P3 p(2) − p(1) = 0 Find a basis for this subspace. Answer: Suppose that p(x) = ax2 + bx + c is a polynomial in S. Then, p(2) = 4a + 2b + c and p(1) = a + b + c, so that p(2) − p(1) = 3a + b. Thus, 3a + b = 0, so b = −3a. Thus, we can write p(x) as p(x) = ax2 − 3ax + c = a(x2 − 3x) + c Th ...
Vectors and Matrices
... and say, respectively, that y equals z, y is greater than or equal to z and that y is greater than z. In the last two cases, we also say that z is less than or equal to y and less than y. It should be emphasized that not all vectors are ordered. For example, if y = (3, 1, −2) and x = (1, 1, 1), then ...
... and say, respectively, that y equals z, y is greater than or equal to z and that y is greater than z. In the last two cases, we also say that z is less than or equal to y and less than y. It should be emphasized that not all vectors are ordered. For example, if y = (3, 1, −2) and x = (1, 1, 1), then ...
MATH 2120 W13 Review 1 1 1. Find the three angles of the triangle
... 16. Determine by inspection(without reducing the matrix) whether the linear system with the augmented matrix below has a unique solution, infinitely many solutions, or no solution. ...
... 16. Determine by inspection(without reducing the matrix) whether the linear system with the augmented matrix below has a unique solution, infinitely many solutions, or no solution. ...
Vectors and Matrices
... A vector is an object with magnitude and direction (velocity, force, acceleration, etc). A scalar is an object with just magnitude (temperature, pressure, age, length). A vector, denoted ~v or v, has no initial point and is often best thought of as at the origin. A vector may be written in component ...
... A vector is an object with magnitude and direction (velocity, force, acceleration, etc). A scalar is an object with just magnitude (temperature, pressure, age, length). A vector, denoted ~v or v, has no initial point and is often best thought of as at the origin. A vector may be written in component ...
Section 1
... We shall denote points, that is, elements of the euclidean plane E2 , by regular upper-case letters. Given a length unit, and two orthogonal lines of reference called the x-axis and the y-axis, each point P ∈ E2 can be represented by an ordered pair of real numbers (x, y) measuring the perpendicular ...
... We shall denote points, that is, elements of the euclidean plane E2 , by regular upper-case letters. Given a length unit, and two orthogonal lines of reference called the x-axis and the y-axis, each point P ∈ E2 can be represented by an ordered pair of real numbers (x, y) measuring the perpendicular ...
