Year 10 Algebra Revision - Mr-Kuijpers-Math
... If h equals the number of hours of labour required to print the leaflets, complete the equation: Cost of leaflets = …………. h + ………….. The sports club has only $1300 budgeted for the printing job. How many hours of labour will this amount afford? The club expects to get 10000 leaflets printed. What is ...
... If h equals the number of hours of labour required to print the leaflets, complete the equation: Cost of leaflets = …………. h + ………….. The sports club has only $1300 budgeted for the printing job. How many hours of labour will this amount afford? The club expects to get 10000 leaflets printed. What is ...
mathematics 10c – outline
... ARRIVE ON TIME – When the bell goes, I expect you to be in your desk, with your books open, ready to start class. If lateness is unavoidable, please enter the classroom with a minimum of disruption. COME PREPARED – Please bring books, pencils, calculators, etc. to class each day. All math is to be d ...
... ARRIVE ON TIME – When the bell goes, I expect you to be in your desk, with your books open, ready to start class. If lateness is unavoidable, please enter the classroom with a minimum of disruption. COME PREPARED – Please bring books, pencils, calculators, etc. to class each day. All math is to be d ...
Rank Nullity Worksheet TRUE or FALSE? Justify your answer. 1
... Solution note: False. The dimension of the image is the rank of A. 2. There exists a surjective linear transformation T : R5 → R4 given by multiplication by a rank 3 matrix. Solution note: False. Surjective means the image is all of R4 , which has dimension 4. The dimension of the image is the rank ...
... Solution note: False. The dimension of the image is the rank of A. 2. There exists a surjective linear transformation T : R5 → R4 given by multiplication by a rank 3 matrix. Solution note: False. Surjective means the image is all of R4 , which has dimension 4. The dimension of the image is the rank ...
Section 2.1 – Points, Lines and Graphs In this section, we look at the
... Remember earlier we looked at points that lie on the x-axis. It turns out that the corresponding y-value is 0. Similarly, if a point lies on the y-axis, its x-coordinate is 0. These two points are called intercepts. So given a linear equation, we always find the intercepts- to find the y-intercept, ...
... Remember earlier we looked at points that lie on the x-axis. It turns out that the corresponding y-value is 0. Similarly, if a point lies on the y-axis, its x-coordinate is 0. These two points are called intercepts. So given a linear equation, we always find the intercepts- to find the y-intercept, ...
Semester Exam Review
... 9.1 Solving Quadratic Equations by Finding Square Roots Square Root—If b2 = a then b is a square root of a. Ex. If 32 = 9, then 3 is a square root of 9 Positive Square Roots—the square root that is a positive number. Ex. 9 3 , 3 is a positive square root of 9 Negative Square Root—the square root t ...
... 9.1 Solving Quadratic Equations by Finding Square Roots Square Root—If b2 = a then b is a square root of a. Ex. If 32 = 9, then 3 is a square root of 9 Positive Square Roots—the square root that is a positive number. Ex. 9 3 , 3 is a positive square root of 9 Negative Square Root—the square root t ...
Lab 2 solution
... (a) Write down the trace of A. Solution: tr(A) = 1. (b) Are the columns of A linearly independent? Justify your answer. Solution: The columns of A are not linearly independent: the second column is the sum of the first and third. (c) Find the rank of A. Solution: The first and third columns of A are ...
... (a) Write down the trace of A. Solution: tr(A) = 1. (b) Are the columns of A linearly independent? Justify your answer. Solution: The columns of A are not linearly independent: the second column is the sum of the first and third. (c) Find the rank of A. Solution: The first and third columns of A are ...
Summary of week 6 (lectures 16, 17 and 18) Every complex number
... (where (u1 , u2 , . . . , un ) is any orthogonal basis for U ) that P is a linear map. We can use orthogonal projections to show that every finite-dimensional inner product space has an orthogonal basis. More generally, suppose that V is an inner product space and U1 ⊂ U2 ⊂ · · · Ud is an increasing ...
... (where (u1 , u2 , . . . , un ) is any orthogonal basis for U ) that P is a linear map. We can use orthogonal projections to show that every finite-dimensional inner product space has an orthogonal basis. More generally, suppose that V is an inner product space and U1 ⊂ U2 ⊂ · · · Ud is an increasing ...
§1.3 Lines and Linear Functions
... point (0, b), called the y-intercept of the line. It is called the slope-intercept form of the equation of the line. ...
... point (0, b), called the y-intercept of the line. It is called the slope-intercept form of the equation of the line. ...
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.