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["Find Average of 4 Weighted Grades"]
["Weights",0.2,0.25,0.25,{"$f":"1-SUM(B2:D2)","v":0.30000000000000004}]
["Scores",80,85,90,100,"Average"]
["Product",{"$f":"B2*B3","v":16},{"$f":"C2*C3","v":21.25},22.5,30.000000000000004,{"$f":"SUM(B4:E4)","v":89.75},"<-- SUM"]
[null,null,null,null,null,{"$f":"SUMPRODUCT(B2:E2,B3:E3)","v":89.75},"<-- SUMPRODUCT"]
[null,null,null,null,null,{"$f":"MMULT(B2:E2,TRANSPOSE(B3:E3))","v":89.75},"<-- Matrix Multiply"]
["Transposed Array using TRANSPOSE:"]
[{"$f":"TRANSPOSE(A2:E4)","v":"Weights"},"Scores","Product",null,"Average"]
[0.2,80,16,null,{"$f":"SUM(C9:C12)","v":89.75},"<-- SUM"]
[0.25,85,21.25,null,{"$f":"SUMPRODUCT(B9:B12,A9:A12)","v":89.75},"<-- SUMPRODUCT"]
[0.25,90,22.5,null,{"$f":"MMULT(B2:E2,B9:B12)","v":89.75},{"$f":"getformula(E11)","v":"<--  =MMULT(B2:E2,B9:B12)"}]
[0.30000000000000004,100,30.000000000000004,null,{"$f":"MMULT(TRANSPOSE(A9:A12),B9:B12)","v":89.75},{"$f":"getformula(E12)","v":"<--  =MMULT(TRANSPOSE(A9:A12),B9:B12)"}]
[]
["Find Average of 4 Weighted Grades for 3 People"]
["Weights",0.2,0.25,0.25,{"$f":"1-SUM(B15:D15)","v":0.30000000000000004}]
["Mary",80,85,90,100]
["John",75,80,85,95]
["Kim",70,75,80,90,"Average"]
[{"$f":"\"Product \"&A16","v":"Product Mary"},{"$f":"B$15*B16","v":16},{"$f":"C$15*C16","v":21.25},22.5,30.000000000000004,{"$f":"SUM(B19:E19)","v":89.75},"<--SUM"]
[{"$f":"\"Product \"&A17","v":"Product John"},{"$f":"B$15*B17","v":15},20,21.25,28.500000000000004,{"$f":"SUM(B20:E20)","v":84.75},"<--SUM"]
["Product Kim",14,18.75,20,27.000000000000004,79.75,"<--SUM"]
[]
["Using MMULT and TRANSPOSE"]
[{"$f":"A16","v":"Mary"},{"$f":"MMULT(B16:E18,TRANSPOSE(B15:E15))","v":89.75},{"$f":"getformula(B24)","v":"<--  =MMULT(B16:E18,TRANSPOSE(B15:E15))"}]
[{"$f":"A17","v":"John"},84.75]
["Kim",79.75]
[]
["Matrix Multiply with MMULT"]
[null,"Order is important: AB ≠ BA"]
[null,"Matrix size is given as #rows by #columns (down x across)"]
[null,"Examples: Below shows A times B = C   or   C=AB"]
[null,null,"# of Columns of A must = # of Rows of B"]
[null,null,"Size of C will be # of Rows in A by # Columns in B"]
[null,null,"Array -->","A","B","C"]
[null,null,"Size -->","2 x 5","5 x 3","2 x 3"]
[null,null,"Size -->","1 x 7","7 x 2","1 x 2"]
[null,null,"Size -->","60 x 1","1 x 1","60 x 1"]
[null,null,"Size -->","1 x 60","1 x 1","Cant Do!"]
[null,null,"Size -->","1 x 1","1 x 60","1 x 60"]
[]
[]
[]
[]
[]
[]
["#SPILL! Error: Results when target array is not empty!"]
[]
[null,{"$f":"MMULT(B16:E18,TRANSPOSE(B15:E15))","v":{"$error":"#VALUE!"}},{"$f":"getformula(B48)","v":"<--  =MMULT(B16:E18,TRANSPOSE(B15:E15))"}]
[]
[null,"xxxxxxx","<-- Cell must be empty to allow array formula to \"spill\""]
[]
[null,"Note that the older version of the array function is entered"]
[null,"with Ctrl-Shift-Enter and shows curly braces - {…}:"]
[]
[null,{"$f":"MMULT(B16:E18,TRANSPOSE(B15:E15))","v":89.75},{"$f":"getformula(B55)","v":"<--  {=MMULT(B16:E18,TRANSPOSE(B15:E15))}"}]
[null,84.75]
[null,79.75]