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bernoli123
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show that if all the row sums of a matrix A belong to C (nxm) are zeroes, then A is singular.
Hint. Observe that Ax=0 for x=[1 1 ...1]T
Hint. Observe that Ax=0 for x=[1 1 ...1]T
When the row sums of a matrix belong to C, it means that all the values obtained by adding up the elements in each row of the matrix are complex numbers. In other words, the sum of each row is a complex number.
Yes, a matrix can have row sums that do not belong to C. This means that at least one of the row sums is not a complex number, and therefore does not satisfy the condition for all row sums to belong to C.
When all row sums of a matrix belong to C, it indicates that the matrix is a complex matrix, meaning that it contains complex numbers as its elements. This can have important implications in mathematical operations and applications of the matrix.
To prove that all row sums of a matrix belong to C, one can use the definition of a complex matrix and the properties of complex numbers. This involves adding up the elements in each row and showing that the result is a complex number.
In addition to all row sums belonging to C, a matrix must also have complex numbers as its elements in order to be considered a complex matrix. This means that at least one element in the matrix must have a real and imaginary part.