Practice Methods To Find Inverse (21.4.3) - Linear Algebra - Mathematics (Civil Engineering -1)

Practice: Methods to Find Inverse

Lesson 21.4.3Linear Algebra

Practise this section

9 questions

Flashcard drill
4 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Define what it means for a matrix to have an inverse.
Show hintHide hint
Think about the identity matrix.
Question 2.
What is the condition for a matrix to be non-singular?
Show hintHide hint
Recall the property of determinants.
3Question 3.
What is the formula for the inverse using the adjoint method?
- A⁻¹ = adj(A)/det(A)
- A⁻¹ = det(A)/adj(A)
- A⁻¹ = A*adj(A)
Show hintHide hint
Recall the roles of adjugate and determinant.
4Question 4.
True or False: A singular matrix has an inverse.
- True
- False
Show hintHide hint
Think about the determinant's role.
Question 5.
Given the matrix A = $\begin{bmatrix} 2 & 4 \\ 1 & 3 \end{bmatrix}$ , find the inverse using both methods: adjoint and Gauss-Jordan.
Show hintHide hint
Calculate determinant first, for both methods.
Question 6.
For a 4x4 matrix B, apply Gauss-Jordan elimination and find the inverse, showing each step explicitly. Consider B = $\begin{bmatrix} 1 & 2 & 3 & 4 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix}$ .
Show hintHide hint
Use row swaps and scaling as necessary.

5 more questions in this section. Enroll free to practise them all.