Use Cramer's rule to solve the systems in Exercises 22 through 24.
In matrices, Cramer's rule expresses the solution in terms of the determinants of the coefficient matrix (i.e., for a square matrix) and of matrices obtained from it by replacing one column by the column vector of right-hand-sides of the equations.
Using Cramer's rule, we solve:
In Exercises 5 through 40, find the matrix of the given linear transformation with respect to the given basis. If no basis is specified, use standard basis: for ,
for and for, . For the space of upper triangular matrices, use the basis
Unless another basis is given. In each case, determine whether is an isomorphism. If isn’t an isomorphism, find bases of the kernel and image of and thus determine the rank of .
21. from to with respect to the basis .
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