Math / Algebra

Question(a) Find the eigenvalues of for
Eigenvalues of $A=\left[\begin{array}{rrrr} 2 & 1 & 4 & 3 \\ 0 & 14 & 3 & 8 \\ 0 & 0 & 18 & 9 \\ 0 & 0 & 0 & 7 \end{array}\right]$ are: $\square$ 졸 $\square$ 줘몯 $\square$ $\square$ (in increasing order) The entry boxes with a small icon beside them are designed to accept numbers or formulas. Help | Switch to Equation Editor

Studdy Solution

STEP 1

What is this asking? Find the eigenvalues of a triangular matrix, and list them from smallest to largest. Watch out! Eigenvalues aren't always integers!
Don't overthink this one, the setup is straightforward.

STEP 2

1. Recognize the matrix type
2. Extract the eigenvalues

STEP 3

Hey everyone!
Look closely at this matrix!
It's an upper triangular matrix.
That means all the entries below the main diagonal are zero.
This makes finding the eigenvalues super easy!

STEP 4

For an upper triangular matrix, the eigenvalues are just the entries along the main diagonal.
Let's grab those values!
They are $\mathbf{2}$ , $\mathbf{14}$ , $\mathbf{18}$ , and $\mathbf{7}$ .

STEP 5

Now, let's arrange them in increasing order as the problem asks.
We have $\mathbf{2}$ , $\mathbf{7}$ , $\mathbf{14}$ , and $\mathbf{18}$ .
Awesome!

STEP 6

The eigenvalues, in increasing order, are $\mathbf{2}$ , $\mathbf{7}$ , $\mathbf{14}$ , and $\mathbf{18}$ .

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Studdy Solution

STEP 1

What is this asking? Find the eigenvalues of a triangular matrix, and list them from smallest to largest. Watch out! Eigenvalues aren't always integers!
Don't overthink this one, the setup is straightforward.

STEP 2

1. Recognize the matrix type
2. Extract the eigenvalues

STEP 3

Hey everyone!
Look closely at this matrix!
It's an upper triangular matrix.
That means all the entries below the main diagonal are zero.
This makes finding the eigenvalues super easy!

STEP 4

For an upper triangular matrix, the eigenvalues are just the entries along the main diagonal.
Let's grab those values!
They are $\mathbf{2}$ , $\mathbf{14}$ , $\mathbf{18}$ , and $\mathbf{7}$ .

STEP 5

Now, let's arrange them in increasing order as the problem asks.
We have $\mathbf{2}$ , $\mathbf{7}$ , $\mathbf{14}$ , and $\mathbf{18}$ .
Awesome!

STEP 6

The eigenvalues, in increasing order, are $\mathbf{2}$ , $\mathbf{7}$ , $\mathbf{14}$ , and $\mathbf{18}$ .

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Studdy Solution

STEP 1

What is this asking? Find the eigenvalues of a triangular matrix, and list them from smallest to largest. Watch out! Eigenvalues aren't always integers!Don't overthink this one, the setup is straightforward.

STEP 2

1. Recognize the matrix type2. Extract the eigenvalues

STEP 3

Hey everyone!Look closely at this matrix!It's an **upper triangular matrix**.That means all the entries *below* the main diagonal are **zero**.This makes finding the eigenvalues super easy!

STEP 4

For an **upper triangular matrix**, the eigenvalues are just the entries along the main **diagonal**.Let's grab those values!They are 2\mathbf{2}2, 14\mathbf{14}14, 18\mathbf{18}18, and 7\mathbf{7}7.

STEP 5

Now, let's **arrange** them in increasing order as the problem asks.We have 2\mathbf{2}2, 7\mathbf{7}7, 14\mathbf{14}14, and 18\mathbf{18}18.Awesome!

STEP 6

The eigenvalues, in increasing order, are 2\mathbf{2}2, 7\mathbf{7}7, 14\mathbf{14}14, and 18\mathbf{18}18.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

What is this asking? Find the eigenvalues of a triangular matrix, and list them from smallest to largest. Watch out! Eigenvalues aren't always integers!
Don't overthink this one, the setup is straightforward.

1. Recognize the matrix type
2. Extract the eigenvalues

Hey everyone!
Look closely at this matrix!
It's an upper triangular matrix.
That means all the entries below the main diagonal are zero.
This makes finding the eigenvalues super easy!

For an upper triangular matrix, the eigenvalues are just the entries along the main diagonal.
Let's grab those values!
They are $\mathbf{2}$ , $\mathbf{14}$ , $\mathbf{18}$ , and $\mathbf{7}$ .

Now, let's arrange them in increasing order as the problem asks.
We have $\mathbf{2}$ , $\mathbf{7}$ , $\mathbf{14}$ , and $\mathbf{18}$ .
Awesome!

The eigenvalues, in increasing order, are $\mathbf{2}$ , $\mathbf{7}$ , $\mathbf{14}$ , and $\mathbf{18}$ .