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Matrix Scalar Multiplication, 1–3 Rows & Columns

Multiply every entry of a matrix by one real scalar, with selectable dimensions through 3 × 3 and reversible nonzero-factor calculations.

  • Formula & worked example
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. 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

Multiplying [[2, −3], [0, 5]] by −2 gives [[−4, 6], [0, −10]]. Multiplication by zero gives zero in every populated entry.

Bᵢⱼ = k × Aᵢⱼ

Worked example

Enter these known values and leave the other values blank.

A (1, 1)
2
A (1, 2)
-3
A (2, 1)
0
A (2, 2)
5
Shared scalar k
-2
Result (1, 1)
-4
Result (1, 2)
6
Result (2, 1)
0
Result (2, 2)
-10

Assumptions and limitations

  • The selected matrix may contain one, two or three rows and columns. Every populated entry uses the same scalar k.
  • Negative and fractional scalars are supported. Zero is valid for forward multiplication; it does not allow recovery of the original matrix from the zero result.
  • For a reverse calculation, provide enough consistent values to identify the desired entry or scalar. A zero known denominator cannot determine a unique missing factor.
  • Reducing the displayed dimensions retains hidden entries. Expand the dimensions again to edit them.

Common questions

Can I recover an input entry from the result?

Yes, when k is nonzero: divide that result entry by k. If k is zero, every possible original entry has the same zero product, so it cannot be uniquely recovered.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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