Page 143 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

Prove: The equation of the line through the distinct points and can be written as
29.

Prove: , , and are collinear points if and only if
30.

31. is an “upper triangular” block matrix, where and are square matrices, then
(a)
If

. Use this result to evaluate for

(b) Verify your answer in part (a) by using a cofactor expansion to evaluate .

Prove that if A is upper triangular and is the matrix that results when the ith row and th column of A are deleted,
32. then is upper triangular if .

What is the maximum number of zeros that a matrix can have without having a zero
33. determinant? Explain your reasoning.

Let A be a matrix of the form
34.

How many different values can you obtain for by substituting numerical values (not

necessarily all the same) for the *'s? Explain your reasoning.

Indicate whether the statement is always true or sometimes false. Justify your answer by giving
35. a logical argument or a counterexample.

(a) is a diagonal matrix for every square matrix .