Which of the following is true? (1) Either the row vectors or the column vectors of a square matrix are linearly independent. (11) A matrix with linearly independent row vectors and linearly independent column vectors is square. (III) Adding one additional column to a matrix increases its rank(or lead term) by one. (IV) The nullity of a square matrix with linearly dependent rows is at least one. (V) If A is square and AX = b is inconsistent for some vector b, then the nullity of A is zero. O (1) O (1) (III) O (IV)

Question

Can you answer these question please ?

Which of the following is true?
(1) Either the row vectors or the column vectors of a square matrix
are linearly independent.
(11) A matrix with linearly independent row vectors and linearly
independent column vectors is square.
(III) Adding one additional column to a matrix increases its rank(or lead
term) by one.
(IV) The nullity of a square matrix with linearly dependent rows is
at least one.
(V) If A is square and AX = b is inconsistent for some vector b,
then the nullity of A is zero.
O (1)
O (1)
(III)
O (IV)
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Transcribed Image Text

Which of the following is true? (1) Either the row vectors or the column vectors of a square matrix are linearly independent. (11) A matrix with linearly independent row vectors and linearly independent column vectors is square. (III) Adding one additional column to a matrix increases its rank(or lead term) by one. (IV) The nullity of a square matrix with linearly dependent rows is at least one. (V) If A is square and AX = b is inconsistent for some vector b, then the nullity of A is zero. O (1) O (1) (III) O (IV)

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