MAT-2240 Midterm: MATH 2240 App State summer2006 Exam2 answer key
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Math 250 section b1 summer 2006: (12pts): determinants. (a) compute the determinant of det. Finally, use the formula for a 2 2 determinant and you"re done. det. 3 4(cid:21)(cid:19) = ( 2)( 3)(1)( 2)[1(4) 3(2)] = ( 2)( 3)(1)( 1)2+12det(cid:18)(cid:20)1 2. 3 4 ( 2)( 1)3+4(3)det ( 2)( 3)(1)( 2)( 2) = 24 (b) compute the determinant of. The determinant of a lower-triangular matrix is the just the product of its diagonals. Thus the determinant of this matrix is 1(2)(2)1 = 4. (c) find all values of c such that the following matrix is not invertible: . Then use the formula for a 2 2 determinant. det . = ( 1)2+2c det(cid:18)(cid:20)1 2 c 4(cid:21)(cid:19) = c[1( 4) c( 2)] = c( 4+2c) = 2c(c 2) A matrix is invertible if and only if its determinant is nonzero. Thus this matrix has no inverse if and only if 2c(c 2) = 0.
