Matrices

Matrices, in essence, are orderly setups of numbers, symbols, or expressions, organized in a pattern of rows and columns. They serve as a key instrument in the field of linear algebra and find vast applications in various domains such as mathematics, physics, engineering, and computer science. The operations that can be performed on matrices encompass addition, subtraction, multiplication, and the computation of the determinant or inverse.

Solving

Given the matrix A=[3241], calculate the inverse of matrix A.
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Simplifying Matrices

Given matrices A = [234−1] and B = [15−23], find the matrix (2A - 3B).
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Solving the System of Equations Using an Inverse Matrix

Given matrices A = [2347] and B = [12], solve for X in the system of equations AX = B using the inverse matrix method.
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Finding the Dimensions

What are the dimensions of the matrix A=(123456789101112)?
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Multiplication by a Scalar

If A=[2413], find the result of the scalar multiplication 5A.
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Multiplication

If A=[13] and B=[24], what is the product of A and B?
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Subtraction

Given two 3x3 matrices, A = [123456789] and B = [987654321], what is the result of A - B?
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Finding the Determinant of the Resulting Matrix

Find the determinant of the matrix A=[234156789]
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Finding the Inverse of the Resulting Matrix

Find the inverse of the matrix A=(23 45)
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Finding the Identity Matrix

Given the matrix A=[3423], find the matrix B such that AB=I, where I is the identity matrix.
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Finding the Scalar multiplied by the Identity Matrix

Find the result of the scalar 5 multiplied by the 2x2 identity matrix.
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Addition

If Matrix A is [23  45  67] and Matrix B is [12  34  56], what is A + B?
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Finding the Determinant of a 2x2 Matrix

Find the determinant of the 2x2 matrix [4235].
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Finding the Determinant of a 3x3 Matrix

Find the determinant of the 3x3 matrix A=[123456789]
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Finding the Determinant of Large Matrices

Find the determinant of the matrix \nA=[5213432112343125]
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Inverse of a 2x2 Matrix

Find the inverse of the matrix A=[3425]
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Finding the Transpose

Find the transpose of the matrix A=[123456789]
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Finding the Adjoint

Find the adjoint of the matrix A=[123045006].
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Finding the Cofactor Matrix

Find the cofactor matrix of the following 3x3 matrix: A=[123045106]
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Null Space

Find the null space of the matrix A=[123 456 789]
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Finding the Basis and Dimension for the Column Space of the Matrix

Find the basis and dimension for the column space of the matrix A=[123 456 789]
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Finding the Basis and Dimension for the Row Space of the Matrix

Find the basis and dimension for the row space of the matrix A=[24−212−136−3]
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Finding the LU Decomposition of a Matrix

Find the LU Decomposition of the matrix A=[4363]
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Popular Problems

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