Linear Algebra | Proveiff Study

prove that following system of linear equations has infinite number of solutions

By SK Math Expert July 9, 2021Linear Algebrasystem of linear equations

Question : Prove that following system of linear equations has infinite number of solutions 3x-y+2z=4 9x-7y+z=-2 Solution : Given system of linear equations 3x-y+2z=4 (1) 9x-7y+z=-2 (2) Writing equations (1)…

What is F(x)F(y) for the given matrix F(x)

By SK Math Expert July 9, 2021Linear Algebraproperties of matrices

Introduction: Here we shall find F(x)F(y) for the given matrix F(x). Question : If \[F(x)\ =\left(\begin{matrix}cos(x)\ &-sin(x)\ &0\\sin(x)&cos(x)&0\\0&0&1\end{matrix}\right)\] then F(x)F(y) is equal to \[F\left(x+y\right)\] \[F\left(x-y\right)\] \[F\left(x\right)+F\left(y\right)\] \[F\left(x\right)-F\left(y\right)\] Solution : Given…

vector space definition and examples

vector space definition and examples

By SK Math Expert June 7, 2021Linear AlgebraVector Space definiton and Examples

Introduction to Vector Space: This world is full with many types of sets. Some sets satisfy a collection of properties and some of them fails to satisfy. Vector space is…

Find eigen values of the matrix [1 -1;0 4]

By SK Math Expert June 2, 2021Linear Algebraeigen values and eigen vectors

Introduction : Here we shall find eigen values of the matrix [1 -1;0 4]. Eigen values of a matrix are numbers that satisfies characteristic equation of the matrix. Question :…

Find eigen values and eigen vectors of a 2 by 2 matrix

By SK Math Expert April 4, 2021Linear Algebraeigen values and eigen vectors of a matrix examples

Introduction: In this solution, we will know how to Find eigen values and eigen vectors of a 2 by 2 matrix. A 2 by 2 matrix is A =[2 -1;-3…

What is the sum of other two eigen values of a matrix?

By SK Math Expert March 25, 2021Linear Algebraeigen values of a matrix

Introduction: In this post, we will learn the step by step working rule to know What is the sum of other two eigen values of a matrix? If one eigen…

What is top row of R^-1 ?

By SK Math Expert March 24, 2021Linear Algebraproperties of inverse of matrices

Introduction: In this post , we will explain the way to answer the question What is top row of R^-1 ? for a given matrix R? Question: If R =…

If A is skew symmetric matrix then what is A^2?

By SK Math Expert March 24, 2021Linear Algebraproperties of symmetric matrices

Introduction: In this post , we will discuss the step by step analysis of the question If A is skew symmetric matrix then what is A^2? Question: if A is…

What is Atr(B)-Btr(A)?

By SK Math Expert March 24, 2021Linear Algebraproperties of symmetric matrices

Introduction: In this post we present the solution of the question What is Atr(B)-Btr(A)? if A and B are symmetric matrices of the same order. Question : If A and…

Let T:R^3->R^2 be linear transformation defined by T(x,y,z) = {x+y,x-z} then what is dimension of null space of T ?

By SK Math Expert March 24, 2021Linear Algebranull spaces

Introduction: In this article, we will write and explain the solution of the question Let T:R^3->R^2 be linear transformation defined by T(x,y,z) = {x+y,x-z} then what is dimension of null…