Matrices

Simplifying Matrices

A = (\begin{matrix} 3 & 5 \\ - 1 & 2 \end{matrix})

and

B = (\begin{matrix} 2 & - 1 \\ 3 & 4 \end{matrix})

, find the matrix

C

such that

C = 2 A - 3 B

More examples

Finding the Variables

2. Calcule os termos desconhecidos: a)

(\begin{array}{cc} x & 3 \\ 5 & 2 y \end{array}) = (\begin{array}{cc} 6 & 3 \\ 5 & 8 \end{array})

More examples

Finding the Dimensions

What are the dimensions of the matrix

A = [\begin{array}{ccc} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{array}]

More examples

Multiplication by a Scalar

A = [\begin{matrix} 2 & 3 \\ 4 & 5 \end{matrix}]

, find the result of the scalar multiplication

3 A

More examples

Multiplication

Given two matrices

A = [\begin{matrix} 2 & 3 \\ 1 & 4 \end{matrix}]

and

B = [\begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix}]

, find the product

A B

More examples

Subtraction

Given two 2x2 matrices A =

[\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}]

and B =

[\begin{matrix} 5 & 6 \\ 7 & 8 \end{matrix}]

, what is the result of A - B?

More examples

Finding the Determinant of the Resulting Matrix

Find the determinant of the following matrix: \n

A = [\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}]

More examples

Finding the Inverse of the Resulting Matrix

If matrix

A = [\begin{matrix} 1 & 2 \\ 3 & 4 \end{matrix}]

, what is

A^{- 1}

, the inverse of matrix A?

More examples

Finding the Identity Matrix

A = [\begin{matrix} 2 & 3 \\ 4 & 5 \end{matrix}]

, find the matrix

B

such that

A B = I

where

I

is the identity matrix.

More examples

Addition

Given two matrices,

A = [\begin{matrix} 3 & 4 \\ 2 & 1 \end{matrix}]

and

B = [\begin{matrix} - 1 & 2 \\ 3 & - 2 \end{matrix}]

, find the result of

A + B

More examples

Simplifying the Matrix Operation

Given matrices A =

[\begin{matrix} 2 & 3 \\ 4 & - 1 \end{matrix}]

and B =

[\begin{matrix} 1 & 2 \\ 3 & 1 \end{matrix}]

, compute the product AB.

More examples

Finding the Determinant of a 2x2 Matrix

Find the determinant of the following 2x2 matrix:

[\begin{matrix} 5 & 3 \\ 2 & 4 \end{matrix}]

More examples

Finding the Determinant of a 3x3 Matrix

Find the determinant of the 3x3 matrix:

A = [\begin{matrix} 2 & 5 & - 3 1 & - 2 & 2 0 & 5 & - 1 \end{matrix}]

More examples

Finding the Determinant of Large Matrices

Find the determinant of the following 4x4 matrix:

A = (\begin{matrix} 3 & 2 & 1 & 4 \\ 0 & 1 & 0 & 2 \\ 1 & 0 & 2 & 1 \\ 0 & 1 & 0 & 1 \end{matrix})

More examples

Inverse of a 2x2 Matrix

Find the inverse of the 2x2 matrix

A = [\begin{matrix} 3 & 4 \\ 2 & 1 \end{matrix}]

More examples

Inverse of an nxn Matrix

Find the inverse of the matrix

A = [\begin{matrix} 1 & 2 3 & 4 \end{matrix}]

More examples

Finding the Cofactor Matrix

Find the cofactor matrix of the given 3x3 matrix A = [[1, 2, 3], [0, 4, 5], [1, 0, 1]]

More examples

Null Space

Find the null space of the following matrix.

A = [\begin{matrix} 1 & 2 & - 1 2 & 4 & - 2 - 1 & - 2 & 1 \end{matrix}]

More examples

Finding the Pivot Positions and Pivot Columns

Find the pivot positions and pivot columns of the following matrix,

[\begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix}]

More examples

Finding the Basis and Dimension for the Column Space of the Matrix

Find the basis and the dimension of the column space for the following matrix

A = [\begin{matrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 \end{matrix}]

More examples

Finding the Basis and Dimension for the Row Space of the Matrix

Given the matrix

A = [\begin{matrix} 1 & 2 & 3 \\ 2 & 4 & 6 \\ 3 & 6 & 9 \end{matrix}]

, find the basis and dimension for the row space of the matrix.

More examples

Simplifying Matrices

Finding the Variables

Finding the Dimensions

Multiplication by a Scalar

Multiplication

Subtraction

Finding the Determinant of the Resulting Matrix

Finding the Inverse of the Resulting Matrix

Finding the Identity Matrix

Addition

Simplifying the Matrix Operation

Finding the Determinant of a 2x2 Matrix

Finding the Determinant of a 3x3 Matrix

Finding the Determinant of Large Matrices

Inverse of a 2x2 Matrix

Inverse of an nxn Matrix

Finding the Cofactor Matrix

Null Space

Finding the Pivot Positions and Pivot Columns

Finding the Basis and Dimension for the Column Space of the Matrix

Finding the Basis and Dimension for the Row Space of the Matrix

Popular Problems