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  3. (8) true/false: circle either t or f. no justifica

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

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Advance Math

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

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

(b) (T : F) The determinant of A is the product of the pivots inany echelon form U of A, multiplied by (?1)r , where r is thenumber of row interchanges made during row reduction from A toU.

(c) (T : F) Adding a multiple of one row to another does notaffect the determinant of a matrix.

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

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

(f) (T : F) det AT = (?1) det A.

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

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

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

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