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Which of the following is true?

a) The product of the eigenvalues of a matrix is equal to the trace of the matrix

b) The eigenvalues of a skew-symmetric matrix are real

c) A is a nonzero column matrix and B is a nonzero row matrix, then the rank of AB is one

d) A system of linear non-homogeneous equations is consistent if and only if the rank of the coefficient matrix is less than or equal to the rank of the augmented matrix

in Linear Algebra by Boss (32.5k points)
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1 Answer

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C is true.

Column matrix rank is 1

Row matrix rank is 1

When two matrices are multiplied, the product matrix rank is <= min of the two ranks

Therefore product matrix rank is 1
by Junior (545 points)
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