In the Doolittle method, what is the primary goal of matrix decomposition?

• To decompose a matrix into an identity matrix and its inverse.

• To decompose a matrix into a lower triangular matrix and a diagonal matrix.

• To decompose a matrix into a lower triangular matrix and an upper triangular matrix.

• To decompose a matrix into two diagonal matrices.

Which of the following matrices has all 1s on the diagonal in the Doolittle decomposition?

• Matrix A

• Matrix L

• Matrix U

• Matrix D

In the Doolittle method, what type of matrix is U?

• A lower triangular matrix

• An upper triangular matrix

• A diagonal matrix

• A symmetric matrix

Which of the following is the correct order of steps in solving a system of linear equations using Doolittle's method?

• Solve Ux = c, then solve Lc = b

• Solve Ax = b directly

• Decompose A into L and U, then solve Lc = b followed by Ux = c

• Decompose A into L and U, then solve Uc = b followed by Lx = c

Which operation is primarily used to find the elements of matrix U in the Doolittle method?

• Addition

• Subtraction

• Multiplication

• Division

The Doolittle method is particularly useful for solving which of the following?

• Systems of linear equations

• Eigenvalue problems

• Non-linear differential equations

• Optimization problems

When performing Doolittle decomposition, what initial values are assigned to the diagonal elements of matrix L?

• 0

• 1

• 2

• The corresponding elements of matrix A

Which mathematical process is used to find the elements of matrix L below the diagonal in the Doolittle method?

• Addition of the corresponding elements from A and U

• Subtraction of the corresponding elements from A and U

• Division of the corresponding elements from A by U

• Multiplication of the corresponding elements from A and U

In Doolittle decomposition, what condition must matrix A satisfy to ensure the decomposition is possible?

• Matrix A must be symmetric.

• Matrix A must be a diagonal matrix.

• Matrix A must be square and non-singular.

• Matrix A must be positive definite.