Chapter 2.2 Flashcards

0
Q

If A is a square matrix then what can be said of its transpose?

A

det(A) = det(transpose(A))

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1
Q

If A is a square matrix with a row or column of zero’s then

A

Det(A) = 0

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2
Q

Let A be a square matrix, how do the row (or column) operations affect the matrix?

A

1) Row or column multiplied with a scalar k >
det(A) > k*det(A)
2) Row or column interchanged >
det(A) > -det(A)
3) Multiple of one row or column times another >
det(A) > det(A)

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3
Q

Let E be an elementary matrix, what operations yields what determinants?

A
1) Row multiplied with a scalar k >
det(E) = k
2) Two rows interchanged >
det(E) = -1
3) Multiple of one row times another >
det(E) = 1
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4
Q

If A is a square matrix with two proportional rows or two proportional columns then

A

Det(A) = 0

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