Kiplinger’s listed the top 100 public colleges based on many factors. From that list, here is the average debt at graduation for various schools in four selected states. Use a 0.05 significance level to test the claim the average (mean) debt at graduation differs for these four states. Results Table New York Virginia California Pennsylvania 14,734 14,524 13,171 18,105 16,000 15,176 14,431 17,051 14,347 12,665 14,689 16,103 14,392 12,591 13,788 22,400 12,500 18,385 15,297 17,976 State the claim and its opposite. State the Null and alternate hypotheses symbolically. Significance level Find the F test statistic. Find the p-value. State the decision State the conclusion

What can be concluded about T_A if A is an m×n matrix and rank(A)=n?

If T:R^n →R^m is a linear transformation, it can always be induced by what?

Which property states that a linear transformation preserves addition?

A matrix transformation induced by an m×n matrix A is one to one if and only if what condition is met?

How are two transformations S:R^n → R^m and T:R^n → R^m defined as equal?

If a transformation T acts by matrix multiplication of a matrix A, what is T called?

If an m×n matrix A is invertible, what does this imply about the linear transformation T_A:R^n →R^m?

For linear transformations T:R^k →R^n and S:R^n →R^m , how is the composite (S∘T)(x) defined?

What happens to the zero vector under a linear transformation T:R^n → R^m ?