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sauravrt
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What does it mean for a matrix to have rank 0 ( zero) ?
Having a rank of 0 means that the matrix has no linearly independent rows or columns. In other words, all the rows and columns in the matrix can be expressed as linear combinations of each other.
Yes, a matrix can have a rank of 0 even if it is not a zero matrix. This happens when the rows and columns are not linearly independent, meaning they can be reduced to all zeros through row operations.
The rank of a matrix cannot be greater than the number of rows or columns it has. If a matrix has a rank of 0, it means that it has no linearly independent rows or columns, and therefore, the number of rows and columns must be equal.
A matrix with a rank of 0 is not invertible, meaning it does not have an inverse matrix. This is because the columns of a non-invertible matrix are linearly dependent, and cannot form a basis for the vector space.
No, a matrix with a rank of 0 cannot be used to solve systems of equations. This is because a matrix with rank 0 does not have a pivot in any column, meaning it cannot be reduced to row echelon form and therefore cannot be used to solve equations using Gaussian elimination.