Answered

Discover the best answers to your questions with the help of IDNLearn.com. Ask anything and receive well-informed answers from our community of experienced professionals.

Without performing any row operations, explain why the matrix does not have an inverse:

[tex]\[
\begin{bmatrix}
5 & 10 & 6 \\
4 & 8 & -1
\end{bmatrix}
\][/tex]

Choose the correct reason below:
A. The value of the determinant, [tex]\(D\)[/tex], is not 0.
B. The matrix does not have a row or column of all zeros.
C. The matrix is not a square matrix.
D. The value of the determinant, [tex]\(D\)[/tex], is 0.

Sagot :

GinnyAnsweridn
To determine why the matrix
[tex]\[ \left[\begin{array}{rrr} 5 & 10 & 6 \\ 4 & 8 & -1 \end{array}\right] \][/tex]
does not have an inverse, let's analyze its properties step by step.

1. Matrix Type:
- For a matrix to potentially have an inverse, it must be a square matrix. This means it has the same number of rows and columns.
- Here we have a matrix of size 2×3 (2 rows and 3 columns).

2. Square Matrix Requirement:
- A 2×3 matrix is not a square matrix since the number of rows (2) is not equal to the number of columns (3).
- Only square matrices (like 2×2, 3×3, and so on) are candidates for having an inverse.

Therefore, since the given matrix is not a square matrix, it cannot have an inverse. This is a fundamental property in linear algebra related to matrix inversion.

Hence, the correct reason is:

C. The matrix is not a square matrix.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. IDNLearn.com has the solutions to your questions. Thanks for stopping by, and come back for more insightful information.