Exam 1 solutions
... 1.(5pts) Let A be a 6 × 5 matrix. What must a and b be in order to define T : Ra → Rb by T (x) = Ax? If we are trying to compute Ax then x must be a length 5 vector. The result of Ax is a length 6 vector. So a = 5 and b = 6. 2.(5pts) Give an example of a 2 × 2 matrix A which has the following three ...
... 1.(5pts) Let A be a 6 × 5 matrix. What must a and b be in order to define T : Ra → Rb by T (x) = Ax? If we are trying to compute Ax then x must be a length 5 vector. The result of Ax is a length 6 vector. So a = 5 and b = 6. 2.(5pts) Give an example of a 2 × 2 matrix A which has the following three ...
Abstract Vector Spaces and Subspaces
... 1. S, the set of all doubly infinite sequences, with addition and scalar multiplication defined element-wise 2. Pn , the set of all polynomials with real coefficients of degree at most n, with addition and scalar multiplication being the usual addition and constant multiple of functions 3. the set o ...
... 1. S, the set of all doubly infinite sequences, with addition and scalar multiplication defined element-wise 2. Pn , the set of all polynomials with real coefficients of degree at most n, with addition and scalar multiplication being the usual addition and constant multiple of functions 3. the set o ...
Algebra: 7.2.3 Exponential Problem Solving Name
... a. Make a table for the first four terms of each of their sequences. What do you notice? b. How do you think Dwayne explained his method of writing the equation to Wade? c. For the sequence 10.3, 11.5, 12.7, …, Wade wrote t(n) = 9.1 + 1.2n while Dwayne wrote t(n) 10.3 + 1.2(n – 1). Make a table for ...
... a. Make a table for the first four terms of each of their sequences. What do you notice? b. How do you think Dwayne explained his method of writing the equation to Wade? c. For the sequence 10.3, 11.5, 12.7, …, Wade wrote t(n) = 9.1 + 1.2n while Dwayne wrote t(n) 10.3 + 1.2(n – 1). Make a table for ...
Mathematics
... System of' linear equations in two variables, Solution of the system of linear equations (i) Graphically. (ii) By algebraic methods: (a) Elimination by substitution (b) Elimination by equating the co-effcients. ( c) Cross multiplication. Applications of Linear equations in two variables in solving s ...
... System of' linear equations in two variables, Solution of the system of linear equations (i) Graphically. (ii) By algebraic methods: (a) Elimination by substitution (b) Elimination by equating the co-effcients. ( c) Cross multiplication. Applications of Linear equations in two variables in solving s ...
Math 5285 Honors abstract algebra Fall 2007, Vic Reiner
... Math 5285 Honors abstract algebra Fall 2007, Vic Reiner Midterm exam 1- Due Wednesday December 12, in class Instructions: This is an open book, open library, open notes, open web, take-home exam, but you are not allowed to collaborate. The instructor is the only human source you are allowed to consu ...
... Math 5285 Honors abstract algebra Fall 2007, Vic Reiner Midterm exam 1- Due Wednesday December 12, in class Instructions: This is an open book, open library, open notes, open web, take-home exam, but you are not allowed to collaborate. The instructor is the only human source you are allowed to consu ...
with solutions - MIT Mathematics
... Solution. There are many ways to see that the answer is no for both questions. For example, if both sides are zero, then c can be scaled at will. 7. Consider the (filled) cylinder of radius 2 and height 6 with axis of symmetry along the z-axis. Cut the cylinder in half along the y-z plane and keep ...
... Solution. There are many ways to see that the answer is no for both questions. For example, if both sides are zero, then c can be scaled at will. 7. Consider the (filled) cylinder of radius 2 and height 6 with axis of symmetry along the z-axis. Cut the cylinder in half along the y-z plane and keep ...
11.1 Linear Systems
... lies on all three planes, namely (2, 3, 2) , and this is the unique solution to the system. Again, this behavior is typical: a 3 × 3 system usually has exactly one solution, since three planes in R3 typically intersect at a single point. As with the two-variable case, a three-variable system with ex ...
... lies on all three planes, namely (2, 3, 2) , and this is the unique solution to the system. Again, this behavior is typical: a 3 × 3 system usually has exactly one solution, since three planes in R3 typically intersect at a single point. As with the two-variable case, a three-variable system with ex ...
Linear algebra
Linear algebra is the branch of mathematics concerning vector spaces and linear mappings between such spaces. It includes the study of lines, planes, and subspaces, but is also concerned with properties common to all vector spaces.The set of points with coordinates that satisfy a linear equation forms a hyperplane in an n-dimensional space. The conditions under which a set of n hyperplanes intersect in a single point is an important focus of study in linear algebra. Such an investigation is initially motivated by a system of linear equations containing several unknowns. Such equations are naturally represented using the formalism of matrices and vectors.Linear algebra is central to both pure and applied mathematics. For instance, abstract algebra arises by relaxing the axioms of a vector space, leading to a number of generalizations. Functional analysis studies the infinite-dimensional version of the theory of vector spaces. Combined with calculus, linear algebra facilitates the solution of linear systems of differential equations.Techniques from linear algebra are also used in analytic geometry, engineering, physics, natural sciences, computer science, computer animation, and the social sciences (particularly in economics). Because linear algebra is such a well-developed theory, nonlinear mathematical models are sometimes approximated by linear models.