M-221 Midterm: Montana State MATH 221 Det
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Let a, b and c be n n matrices, where. , b = b11 b21 bn1 b12 b22 bn2 b1n b2n bnn. , and c = c11 c21 cn1 c12 c22 cn2 c1n c2n cnn. Let a be a square n n matrix (a) if a has a row of zeros or a column of zeros, then det(a) = 0 (b) det(a) = det(at ) A triangular matrix, upper or lower, is an n n matrix in which all entries above the diag- onal or below the diagonal, respectively, are zero. If a is an n n triangular matrix (upper, lower, or diagonal), then det(a) is the product of the entries on the main diagonal of the matrix. That is, det(a) = a11a22 ann. 3 3 case of theorem 3 (a) ka11 ka12 ka13 a21 a23 a33 a31 a22 a32 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) a11 a12 a13 a21 a22 a23 a31 a32 a33 (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)
