(8) TRUE/FALSE: Circle either T or F. No justification is needed. (a) (T : F) Each...

(8) TRUE/FALSE: Circle either T or F. No justification is needed.

(a) (T : F) Each line in R n is a one-dimensional subspace of R n .

(b) (T : F) The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (−1)r , where r is the number of row interchanges made during row reduction from A to U.

(d) (T : F) det(A + B) = det(A) + det(B).

(e) (T : F) If the columns of A are linearly dependent, then det A = 0.

(f) (T : F) det AT = (−1) det A.

(g) (T : F) The determinant of A is the product of the diagonal entries in A.

(h) (T : F) If det A is zero, then two rows or two columns are the same, or a row or a column is zero.

(i) (T : F) If two row interchanges are made in succession, then the determinant of the new matrix is equal to the determinant of the original matrix.

Solutions

Expert Solution

Colby Messinger answered 1 year ago

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