The characteristic polynomial of a 5x5 matrix is given below. find the eigenvalues and their multiplicities.
λ5-11λ4+18λ3

i know the answer is 0(multiplicity 3), 2(multiplicity 1), 9 (multiplicity 1)

but i have absolutely no idea how to get the answer. a question similiar to this will be on my test. show steps to solve. i often get lost in the vocab.

Step-by-step explanation:

given that the characteristic polynomial of a 5x5 matrix is given below.

The solution is simple

Equate the above 5th degree polynomial in lambda to 0 and solve for lambda

We would have 5 solutions

Equating to 0 and factorising we get

Equate each factor to 0

Since lambda has power 3 , we say that 0 is a root with multiplicity 3

(this means 3 times same value repeated as root)

Other roots are 9 and 1 with multiplicity 1 each.

option: d is correct

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.