For each of the following, determine if the statement is true or false. Provide a short reasoning (one or two sentences). a) If the determinant of a square matrix is zero, then the matrix has either one row or column of zeros. b) If the system A = b is consistent, then detA # 0. c) If the columns of a square matrix A are linearly dependent, then detA = 0. %3D d) If A is a square matrix whose diagonal entries are all zero, then detA = 0.

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For each of the following, determine if the statement is true or false. Provide a short
reasoning (one or two sentences).
a) If the determinant of a square matrix is zero, then the matrix has either one row
or column of zeros.
b) If the system A = b is consistent, then det A + 0.
c) If the columns of a square matrix A are linearly dependent, then detA = 0.
d) If A is a square matrix whose diagonal entries are all zero, then detA = 0.
Transcribed Image Text:For each of the following, determine if the statement is true or false. Provide a short reasoning (one or two sentences). a) If the determinant of a square matrix is zero, then the matrix has either one row or column of zeros. b) If the system A = b is consistent, then det A + 0. c) If the columns of a square matrix A are linearly dependent, then detA = 0. d) If A is a square matrix whose diagonal entries are all zero, then detA = 0.
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