Check the true statements below:

a. a number c is an eigenvalue of a if and only if the equation (a−ci)x=0 has a nontrivial solution x.
b. finding an eigenvector of a might be difficult, but checking whether a given vector is in fact an eigenvector is easy.
c. to find the eigenvalues of a, reduce a to echelon form.
d. a matrix a is not invertible if and only if 0 is an eigenvalue of a.
e. if ax=λx for some vector x, then λ is an eigenvalue of a.

A, b, c, and d have the coordinates (-8, 1), (-2, 4), (-3, -1), and (-6, 5), respectively. which sentence about the points is true? a. a, b, c, and d lie on the same line. b. and are perpendicular lines. c. and are parallel lines. d. and are intersecting lines but are not perpendicular. e. and are parallel lines.

For the equations below which statement is true ? -2x=14 6x=-42

() at a farm, animals are fed bales of hay and buckets of gain. each bale of hay is in the shape of a rectangular prism. the base side lengths 2 feet and 3 feet, and the height is 5 feet. each bucket of grain is a cylinder with diameter of 3 feet. the height of the bucket is 5 feet as the height of bale. a. which is larger in area, the rectangular base of the bale or the circular base of the bucket? explain how you know b. which is larger in volume, the bale or the bucket? explain how you know