If A=[1134],B=[21],C=[−7104],D=[321] and E=[23412−1] Find , if possible, a) A+B , C-A and D-E b)AB, BA , CA , AC , DA , DB , BD , EB , BE and AE c) 7C , -3D and KE

Question

If A=[1134],B=[21],C=[−7104],D=[321] and E=[23412−1]  Find , if possible,  a) A+B , C-A and D-E b)AB, BA , CA , AC , DA , DB , BD , EB , BE and AE c) 7C , -3D and KE

Yusuf Keller · Accepted Answer

Step 1  We can add and subtract matrices only which of them have same order.  For multiplication of two matrices it is necessary that no. of columns of first matrix must be equal to no of rows in second matrix.  Step 2  Here,   A=[1134],B=[21],C=[−7104],D=[321] and E=[23412−1]  a) A+B , order of A is 2×2≠ order of B(2×1)  So, Not possible  C-A  C−A=[−7104]−[1134]=[−7−11−10−34−4]=[−80−30]  C−A=[−80−30]  D-E  D-E have different orders  So,not possible  b) AB  AB=[1134][21]=[2+16+4]=[310]  Hence  AB=[310]  BA here [B]2×1[A]2×2  number of columns of B ≠ number of row in A  So,not possible  CA  CA=[−7104][1134]=[−7+3−7+40+120+16]=[−4−31216]  Hence  CA=[−4−31216]  AC  AC=[1134][−7104]=[−71+4−213+16]=[−75−2119]  Hence,  AC=[−75−2119]  DA  [D]1×3[A]2×2  Number columns in [D] ≠ number rows in [A]  So,not possible DB . Not possible BD. Not possible  EB.[E]2×3[B]2×1  Not possible  BE  [B]2×1[E]2×3  Not possible  AE  AE=[1134][23412−1]=  =[2+13+24−16+49+812−4]=[35310178]  Hence,  AE=[35310178]  (c)7C=7[−7104]=[−497028]

Jeffrey Jordon · Accepted Answer

Answer is given below (on video)

If A=begin{bmatrix}1 & 1 3 & 4 end{bmatrix} , B=begin{bmatrix}2 1 end{bmatrix} ,C=begin{bmatrix}-7 & 1 0 & 4 end{bmatrix},D=begin{bmatrix}3 & 2 & 1 en

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