Answered

At Westonci.ca, we connect you with experts who provide detailed answers to your most pressing questions. Start exploring now! Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

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 :

GinnyAnswer
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 your visit. We're dedicated to helping you find the information you need, whenever you need it. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.