Homework SourseIf A aij is an n times n matrix then ai1Ak1 ai2Ak2 ainA
If A = [a_ij] is an n times n matrix, then a_i1A_k1 + a_i2A_k2 + ... + a_inA_kn = 0 for i notequalto k; a_1jA_1k + a_2jA_2k + ... + a_njA_nk = 0 for j notequalto k. Verify Theorem 3.11 for the matrix A = [-3 -7 -3 2 -5 5 -9 -7 7] by computing a_11A_12 + a_21A_22 + A_31A_32. a_11A_12 = a_21A_22 = a_31A_32 = a_11A_12 + a_21A_22 + a_31A_32 =![If A = [a_ij] is an n times n matrix, then a_i1A_k1 + a_i2A_k2 + ... + a_inA_kn = 0 for i notequalto k; a_1jA_1k + a_2jA_2k + ... + a_njA_nk = 0 for j notequal](/WebImages/33/if-a-aij-is-an-n-times-n-matrix-then-ai1ak1-ai2ak2-aina-1095179-1761577372-0.webp "If A = [a_ij] is an n times n matrix, then a_i1A_k1 + a_i2A_k2 + ... + a_inA_kn = 0 for i notequalto k; a_1jA_1k + a_2jA_2k + ... + a_njA_nk = 0 for j notequal")
Solution
A12 = -49 -21 = -(-70) ; A22 = -21 -27 = -48
A32 = -(21 -63) = 42
a11A12 = 70*(-3) = - 210 ; a21A32 = -7*(-48) = 336 ; a31*A32 = (-3)*(42) = -126
So, a11A12 +a21A32 +a31A32 = -210 +336 -126 =0
