A3 by 3 matrix bis known to have eigenvalues 0, 1, 2. this information is enough to find three of these (give the answers where possible) : (a) the rank of b (b) thedeterminantofbtb (c) theeigenvaluesofbtb (d) the eigenvalues of (b2 + j)-1.

Answer with Step-by-step explanation:

We are given that a matrix B .

The eigenvalues of matrix are 0, 1 and 2.

a.We know that

Rank of matrix B=Number of different eigenvalues

We have three different eigenvalues

Therefore, rank of matrix B=3

b.

We know that

Determinant of matrix= Product of eigenvalues

Product of eigenvalues=

After transpose , the value of determinant remain same.

c.Let  

B=

Transpose of matrix:Rows change into columns or columns change into rows.

After transpose of matrix B

Hence, the eigenvalues of are 0, 1 and 4.

d.Eigenvalue of Identity matrix are 1, 1 and 1.

Eigenvalues of

We know that if eigenvalue of A is

Then , the eigenvalue of is

Therefore, the eigenvalues of are  

The eigenvalues of are 1, and

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x

step-by-step explanation:

last month maria hiked the 5-mile mountain trail a number of times and she hiked the 10-mile canal trail several times. let x represent the number of times she hiked the 5-mile trail, and let y represent the number of times she hiked the 10-mile trail. if she hiked a total of 90 miles, which equation can be used to find the number of times maria hiked each trail? x + y = 90 5x – 10y = 90 90 – 10y = 5x 90 + 10y = 5x