Matrix Manipulation and Vector Span

Whether the vector is longer than the other vectors.

Whether the vector is parallel to the other vectors.

Whether the vector can be expressed as a linear combination of the other vectors.

Whether the vector is perpendicular to the other vectors.

Finding the inverse of the matrix.

Adding all vectors together.

Placing the vectors on one side of the matrix and creating an augmented matrix.

Subtracting the vectors from each other.

You can delete any row.

You can swap rows.

You can add or combine any two rows.

You can scale any row.

To transpose the matrix.

To find the eigenvalues of the matrix.

To achieve reduced row echelon form.

To find the determinant of the matrix.

Scaling the second row and adding it to the first row.

Swapping the first and second rows.

Adding a constant to the first row.

Multiplying the first row by zero.

The solutions for the constants in the linear combination.

The determinant of the matrix.

The inverse of the original matrix.

The transpose of the matrix.

By finding the determinant of the matrix.

By checking if the matrix is invertible.

By substituting the constants back into the linear combination and checking if the result matches the target vector.

By checking if the matrix is symmetric.

There is a unique solution.

There are infinitely many solutions.

The matrix is singular.

There is no solution.

A row with a positive number.

A row with a negative number.

A row with all ones.

A fully zeroed out row.

It means the vector is longer than the other vectors.

It means the vector can be expressed as a linear combination of the other vectors.

It means the vector is parallel to the other vectors.

It means the vector is perpendicular to the other vectors.