Let the matrix
𝑋
be
𝑋
=
[
−
9

4

−
7

𝑘
]
.

For
𝑋
to have
0
as an eigenvalue, what must
𝑘
be?

Question

Let the matrix 
𝑋
 be
𝑋
=
[
−
9
	
4

−
7
	
𝑘
]
.

For 
𝑋
 to have 
0
 as an eigenvalue, what must 
𝑘
 be?

BlackTom AI · Accepted Answer

To determine when X has 0 as an eigenvalue, we need to find when 0 is an eigenvalue of a 2x2 matrix, which occurs precisely when the determinant of X is zero.

Option analysis:
- Option "28
9" (interpreted as the fraction 28/9): This corresponds to solving det(X) = 0. For X = [ [-9, 4], [-7, k] ], the determinant is (-9)*k - (4)*(-7) = -9k + 28. Setting det(X) = 0 gives -9k + 28 = 0, so k = 28/9. Therefore, this option is correct because it matches the required value that makes the determinant zero, ensuring 0 is an eigenvalue.

- There are no additional options provided to evaluate. If another value were present, we would similarly substitute into det(X) = 0 and check whether the resulting k satisfies the equation. In this case, the unique solution to -9k + 28 = 0 is k = 28/9, so any alternative option would be incorrect.

Summary: The determinant condition leads to k = 28/9, so the given option "28
9" is the correct choice. The key idea is that a zero eigenvalue occurs exactly when the determinant is zero for a square matrix, which translates to solving -9k + 28 = 0 for k.

MATH1061/1002/1021 (ND) MATH1061 Canvas Quiz 9

Let the matrix 𝑋 be 𝑋 = [ − 9 4 − 7 𝑘 ] . For 𝑋 to have 0 as an eigenvalue, what must 𝑘 be?

View Explanation

Log in for full answers

Similar Questions

True or False: If 'L' is an eigenvalue for some square matrix, A, then 'L' must also be an eigenvalue for the square matrix A-1.

True or False: If 'L' is an eigenvalue for some square matrix, A, then 'L' must also be an eigenvalue for the square matrix AT.

True or False: Suppose that A is a 3x3 matrix whose eigenvalues are -3, 5 and 1/2. Then it must be the case that A is an invertible matrix.

Question20 Consider the matrix [math]. What are the eigenvalues of this matrix?Select one alternative: 1 and 5 1 and 6 0 and 5 0 and 6 ResetMaximum marks: 1 Flag question undefined

Let the matrix X be X=[−9 4 −7 k]. For X to have 0 as an eigenvalue, what must k be?

Let the matrix X be X=[4 −1 1 k]. For X to have 0 as an eigenvalue, what must k be?

Let the matrix \(X\) be \[X = \left [\begin{matrix}8 & -2\\-6 & k\end{matrix}\right ].\] For \(X\) to have \(0\) as an eigenvalue, what must \(k\) be?

Suppose A is an n×n symmetric positive definite matrix and A=B2. Given that the eigenvalues of A are 18.5 and 9.5, find the eigenvalues of B.

More Practical Tools for Students Powered by AI Study Helper

Homework AI Solver

Stylized AI Paper Writer

Plagiarism Checker Assistant

Citation AI Academic Writing Tool

In-Class Translation Assistant

AI Note Generator

AI Quiz Answers

Past Exam Questions from University Test Bank

Smart Practice Assistant

Adaptive Practice

Making Your Study Simpler