What it measures or solves
A matrix represents a linear transformation or a linked system of coefficients.
Matrix Calculator
Build matrices and solve matrix operations with guided explanations.
Matrix A
Matrix B
Result
Choose an operation to calculate.
Show your work Matrix method
- Choose an operation to see its matrix steps and a verification method.
Linear algebra
Understand the matrix operation calculation
Defining relationship
Dimensions and pivots determine which operations are defined.
Inputs for the matrix operation
InputWhat it means
Matrix AThe primary transformation or coefficient array.
Matrix BA second array or right-hand side when the operation needs one.
DimensionsRows and columns must satisfy the selected operation.
Show your work in four steps
- Write the goal in words: identify the exact matrix operation quantity the question asks you to find.
- List every value needed for the matrix operation relationship with its sign and unit. Put negative values in parentheses and record any interval, angle mode, matrix size, or restriction that changes this calculation.
- Write the linear algebra formula or rule before inserting numbers. Replace each symbol with its matching given value, then calculate one line at a time using the order of operations.
- State the final matrix operation answer with units and the requested rounding. Check it by substitution, an inverse operation, a graph, a size estimate, or a second method before using it elsewhere.
Copy-ready example
A=[[1,2],[3,4]]
det(A)=−2 and A is invertible
How to verify the matrix operation result
- Confirm the result answers the requested matrix operation quantity, not a related intermediate value.
- For this matrix operation problem, check sign, scale, units, domain restrictions, and whether an exact or decimal form is required.
- Change one matrix operation input slightly and confirm the output moves in the direction predicted by the rule above: Dimensions and pivots determine which operations are defined.
Questions about the matrix operation calculator
What does the Matrix Calculator need?
Enter the values named in the matrix operation relationship and include every condition that changes which method or answer is valid.
How should I check a matrix operation result?
Put the matrix operation result back into the defining relationship, then compare its sign, size, units, and limiting behavior with a quick estimate or inverse operation.
Does the Matrix Calculator use a programmed method?
Yes. The Matrix Calculator evaluates its stated linear algebra method directly in the calculator workbench. Optional tutoring is separate and requires a free account.
How to use the Matrix Calculator
Use the interactive workspace first, then connect the output to the mathematical definitions and checks below.
Matrix operations available
Configure matrices from 1×1 through 4×4, then add, subtract, multiply, transpose, calculate a determinant or inverse, and solve compatible systems Ax=B. The result panel explains the selected operation and keeps matrix dimensions visible.
Dimensions determine valid operations
Addition requires equal dimensions. A product A×B exists when the number of columns of A equals the number of rows of B. Determinants and ordinary inverses require square matrices, and an inverse exists only when the determinant is nonzero.
How to verify a matrix result
Check a product entry with one row-by-column dot product. Multiply A by a proposed inverse and look for the identity matrix. For Ax=B, multiply the returned x by A and compare every component with B.
Need a complete explanation?
Send the exact question and your current work to MathGPT for a step-by-step method and an independent check.
Learn the mathematics
Understand linear algebra behind this calculator
A calculator confirms an answer. Working the method yourself is what makes the next problem faster.