Answer:
the rank of matrix B is 2.
Step-by-step explanation:
If a 3 by 3 matrix B is known to have eigenvalues 0, 1, and 2, we can find its rank as follows:
The rank of a matrix is the maximum number of linearly independent rows or columns. In the context of eigenvalues, it’s important to note that the number of non-zero eigenvalues is equal to the rank of the matrix.
Given that the eigenvalues of the 3x3 matrix B are 0, 1, and 2, we can see that two of these eigenvalues are non-zero (1 and 2). Therefore, the rank of matrix B is 2.
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