Free · Matrix operations
Matrix Multiplication with One to Three Rows
Multiply compatible matrices with one to three rows and columns by taking row–column dot products.
- Formula & worked example
- Private in your browser
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
Each output cell is the sum of the first matrix row entries multiplied by the corresponding second matrix column entries.
C_ij=Σ_k A_ik B_kj; columns(A)=rows(B)
Worked example
Enter these known values and leave the other values blank.
- Number of rows
- 3
- Number of columns
- 3
- Number of rows
- 3
- Number of columns
- 3
- a==1==
- 4
- a==2==
- 5
- a==3==
- 6
- b==1==
- 7
- b==2==
- 8
- b==3==
- 9
- c==1==
- 10
- c==2==
- 11
- c==3==
- 12
- x==1==
- 4
- x==2==
- 3
- x==3==
- 2
- y==1==
- 8
- y==2==
- 7
- y==3==
- 6
- z==1==
- 12
- z==2==
- 11
- z==3==
- 10
- c==11==
- 128
- c==12==
- 113
- c==13==
- 98
- c==21==
- 200
- c==22==
- 176
- c==23==
- 152
- c==31==
- 272
- c==32==
- 239
- c==33==
- 206
Assumptions and limitations
- This is ordinary matrix multiplication. The number of columns in the first matrix must equal the number of rows in the second.
- Matrix order matters: AB and BA can differ or one order can be undefined.
- Signed decimals and zero are valid entries. The result is forward only; one product cannot uniquely recover both matrices.
Common questions
Why do the inner dimensions need to match?
Each row–column dot product pairs one entry per shared index k. Without equal inner dimensions, that sum is undefined.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.