Determinants and Cramer's Rule: Videos & Practice Problems

Find the value of the given determinant using the determinant theorems.

Find the value of the given determinant using the determinant theorems.

Solve the system of equations by using Cramer's rule. Use a different method if D = 0.

Solve the system of equations by using Cramer's rule. Use a different method if D = 0.

Work out the given equation:

Work out the given equation:

Evaluate the determinant of the 2x2 matrix:

Evaluate the determinant of the 2x2 matrix:

Evaluate the determinant of the 3x3 matrix: 

For the given matrices, work out the products AB and BA to show if B is the inverse (multiplicative) of A.

For the given matrices, work out the products AB and BA to show if B is the inverse (multiplicative) of A.

For the given matrices, work out the products AB and BA to show if B is the inverse (multiplicative) of A.

Express the following system of equations as AX = B, where A is the coefficient matrix, and B is the constant matrix. Then, solve the system using the given inverse of the coefficient matrix.

Express the following system of equations as AX = B, where A is the coefficient matrix, and B is the constant matrix. Then, solve the system using the given inverse of the coefficient matrix.

Express the following system of equations as AX = B, where A is the coefficient matrix, and B is the constant matrix. Then, solve the system using the given inverse of the coefficient matrix.

For the given matrices, work out the products AB and BA to show if B is the inverse (multiplicative) of A.

For the given matrices, work out the products AB and BA to show if B is the inverse (multiplicative) of A.

For the given matrices, work out the products AB and BA to show if B is the inverse (multiplicative) of A.

Express the following matrix equation as a system of equations:

Express the following matrix equation as a system of equations:

Express the following system of equations as a matrix equation:

Express the following system of equations as a matrix equation: 

Find the multiplicative inverse of the matrix shown by using the formula for A^-1. Also, verify that AA^-1 = I₂ and A^-1A = I₂, where I₂ is a multiplicative identity matrix of order 2.

Find the multiplicative inverse of the matrix shown by using the formula for A^-1. Also, verify that AA^-1 = I₂ and A^-1A = I₂, where I₂ is a multiplicative identity matrix of order 2.

Find the multiplicative inverse of the matrix shown by using the formula for A^-1. Also, verify that AA^-1 = I₂ and A^-1A = I₂, where I₂ is a multiplicative identity matrix of order 2.

The inverse of the coefficient matrix is given. Solve the system of equations using the given equation and the coefficient matrix. 

Evaluate A^-1, Verify your answer by finding AA^-1 = I

Determine whether B is the multiplicative inverse of A by finding the products AB and BA.

Perform the multiplication of the given matrices in either order.

Perform the multiplication of the given matrices.