Find the determinants of the linear transformations in Exercises 17 through 28.
27. , where a and b are arbitrary constants, from the space V spanned by and to V
Therefore, the determinant of the linear transformations is given by,
A determinant is a unique number associated with a square matrix.
A determinant is a scalar value that is a function of the entries of a square matrix.
It is the signed factor by which areas are scaled by this matrix. If the sign is negative the matrix reverses orientation.
Given linear transformation,
For , we have .
So we compute
Obviously is a basis for , so the matrix of that corresponds to is
(For those who have studied multivariable calculus.) Let T be an invertible linear transformation fromto, represented by the matrix M. Letbe the unit square in andits image under T . Consider a continuous functionfromto, and define the function. What is the relationship between the following two double integrals?
Your answer will involve the matrix M. Hint: What happens when, for all?
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