MAT188H1 Midterm: MAT188H1_20169_641483478605mat188tut9sol

• School: UTSG
• Department: Mathematics
• Course: MAT188H1
• Professor: All

Document Summary

Faculty of applied science & engineering, university of toronto. Tutorial problems 9: let a = . 2 4 4 c (a) find det(a). (b) for what values of c is a invertible? (c) for the values of c such that a is invertible, nd det(a 1). Solution: (a) we compute det(a) by cofactor expansion along the second row: det(a) = c det(cid:20)1 1. In our case, it follows from part (a) that a is invertible i 2c + 10 6= 0. A is invertible i c 6= 5. (c) whenever a is invertible (i. e. when c 6= 5), we have det(a 1) = 2c + 10: by row-reducing to upper-triangular form, evaluate det. Solution: using theorem 3 from section 5. 1 along with theorems 1, 2, and 4 from section 5. 2 in the textbook, we perform elementary row operations: This is known as the additive property of the determinant. Note that similar equalities hold for other rows too.