Name: Linear Algebra – 3191 Summer 2012 – Sullivan Homework ...
Name: Linear Algebra – 3191 Summer 2012 – Sullivan Homework ... Name: Linear Algebra – 3191 Summer 2012 – Sullivan Homework ...
(d) If one row of A is multiplied by k to produce B, then det(B) =?? (e) If matrix A has a row of zeros then det(A) =?? (f) If matrix A has two equal rows then det(A) =?? (g) The determinant of a triangular matrix is (h) det(AB) =?? (i) det(A T ) =?? (j) A is invertible if and only if 4. Use cofactor expansion (described in section 3.1) to compute the determinant (Soln) ¡+your solution here+¿ 5 −2 4 0 3 −5 2 −4 7 5. Find a formula for det(r·A) when A is an n×n matrix and r ∈ R. Explain your reasoning. (Soln) ¡+your solution here+¿ 2
(d) If one row of A is multiplied by k to produce B, then det(B) =??<br />
(e) If matrix A has a row of zeros then det(A) =??<br />
(f) If matrix A has two equal rows then det(A) =??<br />
(g) The determinant of a triangular matrix is<br />
(h) det(AB) =??<br />
(i) det(A T ) =??<br />
(j) A is invertible if and only if<br />
4. Use cofactor expansion (described in section 3.1) to compute the determinant<br />
(Soln) ¡+your solution here+¿<br />
<br />
<br />
5<br />
−2 4 <br />
<br />
<br />
0<br />
3 −5<br />
<br />
2<br />
−4 7 <br />
5. Find a formula for det(r·A) when A is an n×n matrix and r ∈ R. Explain your reasoning.<br />
(Soln) ¡+your solution here+¿<br />
2
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