CM222, Linear Algebra Mock Test 3 Solutions 1. Let P2 denote the
... Solution: a), c) Explanation: a) is the definition. c) is the same as a) since the eigenvalues with eigenvalue λ are precisely the non-zero vectors in the null space of A − λI. b) is incorrect, since for example the geometric multiplicity of the eigenvalue 1 for the 2 × 2 identity matrix is 2, but t ...
... Solution: a), c) Explanation: a) is the definition. c) is the same as a) since the eigenvalues with eigenvalue λ are precisely the non-zero vectors in the null space of A − λI. b) is incorrect, since for example the geometric multiplicity of the eigenvalue 1 for the 2 × 2 identity matrix is 2, but t ...
PLP-for-Higher Maths
... I can find the area between a curve and the x-axis I know that there are no negative areas I can find the area between two curves I can solve differential equations ...
... I can find the area between a curve and the x-axis I know that there are no negative areas I can find the area between two curves I can solve differential equations ...
Int Alg II Sec 1-5(part 1) notes Template
... Intermediate Algebra II Section 1-5(part 1) Notes Template I. Objective: To solve inequalities and graph their solutions. II. Teacher activities: A) Hook: Solve the equation: 4x + 2 = -6 B) Solve inequalities the same way you solve equations. Get the variable to the left, then the shading will go ...
... Intermediate Algebra II Section 1-5(part 1) Notes Template I. Objective: To solve inequalities and graph their solutions. II. Teacher activities: A) Hook: Solve the equation: 4x + 2 = -6 B) Solve inequalities the same way you solve equations. Get the variable to the left, then the shading will go ...
Question 1 ......... Answer
... A subspace V of Rn is called a hyperplane if the vectors ~x ∈ V are defined by an equation: a1 x1 + a2 x2 + . . . + an xn = 0, where at least one of the coefficients ai is nonzero. (a) [3 points] How many of the variables xi are free? What is the dimension of a hyperplane in Rn ? (b) [4 points] Expl ...
... A subspace V of Rn is called a hyperplane if the vectors ~x ∈ V are defined by an equation: a1 x1 + a2 x2 + . . . + an xn = 0, where at least one of the coefficients ai is nonzero. (a) [3 points] How many of the variables xi are free? What is the dimension of a hyperplane in Rn ? (b) [4 points] Expl ...
Equation
In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.