Solution.
P = ( 28 35 28 36 37 34 45 36 37 47 32 36 38 47 41 42 40 35 51 56 61 30 33 39 33 78 76 83 ) ; A = ( 1 1 1 1 1 1 1 ) ; P=\begin{pmatrix} 28& 35& 28 &36& 37& 34 &45 \\ 36& 37 &47 &32 &36& 38 &47\\ 41& 42 &40& 35& 51& 56& 61\\ 30& 33 &39& 33& 78& 76 &83 \end{pmatrix};
A=\begin{pmatrix} 1 \\ 1\\ 1\\ 1\\1\\1\\1 \end{pmatrix}; P = ⎝ ⎛ 28 36 41 30 35 37 42 33 28 47 40 39 36 32 35 33 37 36 51 78 34 38 56 76 45 47 61 83 ⎠ ⎞ ; A = ⎝ ⎛ 1 1 1 1 1 1 1 ⎠ ⎞ ;
The product of matrices:
P A = ( 28 35 28 36 37 34 45 36 37 47 32 36 38 47 41 42 40 35 51 56 61 30 33 39 33 78 76 83 ) ( 1 1 1 1 1 1 1 ) = PA=\begin{pmatrix} 28& 35& 28 &36& 37& 34 &45 \\ 36& 37 &47 &32 &36& 38 &47\\ 41& 42 &40& 35& 51& 56& 61\\ 30& 33 &39& 33& 78& 76 &83 \end{pmatrix}\begin{pmatrix} 1 \\ 1\\ 1\\1\\1\\1\\ 1 \end{pmatrix}= P A = ⎝ ⎛ 28 36 41 30 35 37 42 33 28 47 40 39 36 32 35 33 37 36 51 78 34 38 56 76 45 47 61 83 ⎠ ⎞ ⎝ ⎛ 1 1 1 1 1 1 1 ⎠ ⎞ =
= ( 243 273 326 372 ) , =\begin{pmatrix} 243 \\ 273\\ 326\\ 372 \end{pmatrix}, = ⎝ ⎛ 243 273 326 372 ⎠ ⎞ ,
A 1 , 1 = 28 ⋅ 1 + 35 ⋅ 1 + 28 ⋅ 1 + 36 ⋅ 1 + 37 ⋅ 1 + 34 ⋅ 1 + 45 ⋅ 1 = 243 ; A_{
1,1}
=28⋅1+35⋅1+28⋅1+36⋅1+37⋅1+34⋅1+45⋅1=243; A 1 , 1 = 28 ⋅ 1 + 35 ⋅ 1 + 28 ⋅ 1 + 36 ⋅ 1 + 37 ⋅ 1 + 34 ⋅ 1 + 45 ⋅ 1 = 243 ;
A 2 , 1 = 36 ⋅ 1 + 37 ⋅ 1 + 47 ⋅ 1 + 32 ⋅ 1 + 36 ⋅ 1 + 38 ⋅ 1 + 47 ⋅ 1 = 273 ; A_{2,1}=36⋅1+37⋅1+47⋅1+32⋅1+36⋅1+38⋅1+47⋅1=273; A 2 , 1 = 36 ⋅ 1 + 37 ⋅ 1 + 47 ⋅ 1 + 32 ⋅ 1 + 36 ⋅ 1 + 38 ⋅ 1 + 47 ⋅ 1 = 273 ;
A 3 , 1 = 41 ⋅ 1 + 42 ⋅ 1 + 40 ⋅ 1 + 35 ⋅ 1 + 51 ⋅ 1 + 56 ⋅ 1 + 61 ⋅ 1 = 326 ; A_{3,1}=41⋅1+42⋅1+40⋅1+35⋅1+51⋅1+56⋅1+61⋅1=326; A 3 , 1 = 41 ⋅ 1 + 42 ⋅ 1 + 40 ⋅ 1 + 35 ⋅ 1 + 51 ⋅ 1 + 56 ⋅ 1 + 61 ⋅ 1 = 326 ;
A 4 , 1 = 30 ⋅ 1 + 33 ⋅ 1 + 39 ⋅ 1 + 33 ⋅ 1 + 78 ⋅ 1 + 76 ⋅ 1 + 83 ⋅ 1 = 372 ; A_{4,1}=30⋅1+33⋅1+39⋅1+33⋅1+78⋅1+76⋅1+83⋅1=372; A 4 , 1 = 30 ⋅ 1 + 33 ⋅ 1 + 39 ⋅ 1 + 33 ⋅ 1 + 78 ⋅ 1 + 76 ⋅ 1 + 83 ⋅ 1 = 372 ;
B = ( 1 1 1 1 ) ; B=\begin{pmatrix} 1& 1& 1 &1& \end{pmatrix}; B = ( 1 1 1 1 ) ;
B P = ( 1 1 1 1 ) ( 28 35 28 36 37 34 45 36 37 47 32 36 38 47 41 42 40 35 51 56 61 30 33 39 33 78 76 83 ) = BP=\begin{pmatrix} 1& 1& 1 &1& \end{pmatrix}\begin{pmatrix} 28& 35& 28 &36& 37& 34 &45 \\ 36& 37 &47 &32 &36& 38 &47\\ 41& 42 &40& 35& 51& 56& 61\\ 30& 33 &39& 33& 78& 76 &83 \end{pmatrix}= BP = ( 1 1 1 1 ) ⎝ ⎛ 28 36 41 30 35 37 42 33 28 47 40 39 36 32 35 33 37 36 51 78 34 38 56 76 45 47 61 83 ⎠ ⎞ = = ( 135 147 154 136 202 204 236 ) , =\begin{pmatrix} 135&147 & 154&136&202&204& 236 \end{pmatrix}, = ( 135 147 154 136 202 204 236 ) ,
A 1 , 1 = 1 ⋅ 28 + 1 ⋅ 36 + 1 ⋅ 41 + 1 ⋅ 30 = 135 ; A_{1,1}=1\sdot28+1\sdot36+1\sdot41+1\sdot30=135; A 1 , 1 = 1 ⋅ 28 + 1 ⋅ 36 + 1 ⋅ 41 + 1 ⋅ 30 = 135 ;
A 1 , 2 = 1 ⋅ 35 + 1 ⋅ 37 + 1 ⋅ 42 + 1 ⋅ 33 = 147 ; A_{1,2}=1\sdot35+1\sdot37+1\sdot42+1\sdot33=147; A 1 , 2 = 1 ⋅ 35 + 1 ⋅ 37 + 1 ⋅ 42 + 1 ⋅ 33 = 147 ;
A 1 , 3 = 1 ⋅ 28 + 1 ⋅ 47 + 1 ⋅ 40 + 1 ⋅ 39 = 154 ; A_{1,3}=1\sdot28+1\sdot47+1\sdot40+1\sdot39=154; A 1 , 3 = 1 ⋅ 28 + 1 ⋅ 47 + 1 ⋅ 40 + 1 ⋅ 39 = 154 ;
A 1 , 4 = 1 ⋅ 36 + 1 ⋅ 32 + 1 ⋅ 35 + 1 ⋅ 33 = 136 ; A_{1,4}=1\sdot36+1\sdot32+1\sdot35+1\sdot33=136; A 1 , 4 = 1 ⋅ 36 + 1 ⋅ 32 + 1 ⋅ 35 + 1 ⋅ 33 = 136 ;
A 1 , 5 = 1 ⋅ 37 + 1 ⋅ 36 + 1 ⋅ 51 + 1 ⋅ 78 = 202 ; A_{1,5}=1\sdot37+1\sdot36+1\sdot51+1\sdot78=202; A 1 , 5 = 1 ⋅ 37 + 1 ⋅ 36 + 1 ⋅ 51 + 1 ⋅ 78 = 202 ;
A 1 , 6 = 1 ⋅ 34 + 1 ⋅ 38 + 1 ⋅ 56 + 1 ⋅ 76 = 204 ; A_{1,6}=1\sdot34+1\sdot38+1\sdot56+1\sdot76=204; A 1 , 6 = 1 ⋅ 34 + 1 ⋅ 38 + 1 ⋅ 56 + 1 ⋅ 76 = 204 ;
A 1 , 7 = 1 ⋅ 45 + 1 ⋅ 47 + 1 ⋅ 61 + 1 ⋅ 83 = 236 ; A_{1,7}=1\sdot45+1\sdot47+1\sdot61+1\sdot83=236; A 1 , 7 = 1 ⋅ 45 + 1 ⋅ 47 + 1 ⋅ 61 + 1 ⋅ 83 = 236 ;
Answer: P A = ( 243 273 326 372 ) ; PA=\begin{pmatrix} 243 \\ 273\\ 326\\ 372 \end{pmatrix}; P A = ⎝ ⎛ 243 273 326 372 ⎠ ⎞ ;
B P = ( 135 147 154 136 202 204 236 ) . BP=\begin{pmatrix} 135&147 & 154&136&202&204& 236 \end{pmatrix}. BP = ( 135 147 154 136 202 204 236 ) .
Comments