If A has diagonals [2, 0, 2, 0] then the rank of A is*

4

2

Less than 4

Data insufficient/None of the options

To determine the rank of matrix \( A \), we consider that the rank is the maximum number of linearly independent rows or columns. From the given diagonals of matrix \( A \) as \([2, 0, 2, 0]\), we can infer that \( A \) is likely a 4x4 diagonal matrix of the form:

\[
A = \begin{pmatrix}
2 & 0 & 0 & 0 \\
0 & 0 & 0 & 0 \\
0 & 0 & 2 & 0 \\
0 & 0 & 0 & 0
\end{pmatrix}
\]

In a diagonal matrix, the rank is determined by the number of non-zero entries on the diagonal.

- The matrix has two non-zero diagonal entries: 2 and 2.
- Therefore, the rank of this matrix is 2, as there are two linearly independent rows (or columns).

Thus, the correct answer is:

**2**

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Do you want more details or have any questions?

Here are some related questions:
1. How do you compute the rank of any general matrix?
2. How does the presence of zeros on the diagonal affect the rank?
3. Can a diagonal matrix have a rank greater than its dimension?
4. How do you find the rank of a non-diagonal matrix?
5. How does Gaussian elimination help in finding the rank of a matrix?

**Tip:** A matrix's rank gives insight into its dimensional properties, such as how many independent vectors span its column or row space.

If A has diagonals [2, 0, 2, 0] then the rank of A is* 4, 2, Less than 4, Data insufficient/None of the options

Learn how to find the rank of a diagonal matrix with diagonals [2, 0, 2, 0]. This problem focuses on the concept of matrix rank, diagonal matrices, and determining the number of linearly independent rows or columns. Suitable for students in undergraduate linear algebra courses.

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