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Homework Statement
T(2,1)---> (5,2) and T(1,2)--->(7,10) is a linear map on R^2. Determine the matrix T with respect to the basis B= {(3,3),(1,-1)}
Homework Equations
The Attempt at a Solution
matrix = 5 7
2 10 ?
A matrix for a linear map is a mathematical representation of a linear transformation between two vector spaces. It consists of rows and columns of numbers that correspond to the coefficients of the linear map's equations.
A matrix for a linear map is created by organizing the coefficients of the linear map's equations into rows and columns. The number of rows and columns in the matrix will depend on the number of variables and equations in the linear map.
The purpose of using a matrix for a linear map is to simplify the process of solving equations involving linear transformations. By converting the equations into matrix form, we can use various matrix operations to solve for unknown variables.
Yes, a matrix for a linear map can be used for any type of linear transformation, as long as it is between two vector spaces. This includes rotations, reflections, and scaling.
The size of a matrix for a linear map is determined by the dimensions of the vector spaces involved. For example, a linear map between two 3-dimensional vector spaces will have a 3x3 matrix. In general, a linear map between an n-dimensional vector space and an m-dimensional vector space will have an mxn matrix.