Tutorial 6.0: Matrix Operations and Determinants of Square Matrices (Curtin University)

# Topic: Matrix Operations and Determinant of Square Matrices ## Tutorial 6.0 ### 1. A matrix with _n_ rows and _m_ columns has size _n x m_. Write down the size of each of the following matrices. - **A**: 4 x 2 - **B**: 2 x 4 - **C**: 4 x 1 - **D**: 4 x 3 **A** = [2 -3 1] [4 1 0] [ -1 1 3]...

# Topic: Matrix Operations and Determinant of Square Matrices ## Tutorial 6.0 ### 1. A matrix with _n_ rows and _m_ columns has size _n x m_. Write down the size of each of the following matrices. - **A**: 4 x 2 - **B**: 2 x 4 - **C**: 4 x 1 - **D**: 4 x 3 **A** = [2 -3 1] [4 1 0] [ -1 1 3] **B** = [2 3 -7 32] [-1 1 0 5] **C** = [1 0 0] [3 3 1] [5 0 5] [2 -1 -2] **D** = [0 5 0] [0 1 3] [1 0 0] [3 2 1] ### 2. Given: **A** = [2 3 4] [-3 1 2] **B** = [3 3] [1 2] **C** = [2 5 3], [-1 2 1] determine: - **(a)** A + B - **(b)** A - 3B + C - **(c)** 2BC ### 3. If **A** = [3 4] [1 2], **B** = [2 1] [1 0], evaluate: - **(a)** |A| - **(b)** |AB| ### 4. Determine the determinant of [5 2 -1] [6 2 2] [2 2 1] by using Sarrus's Rule and expansion by cofactors method. ### 5. Given that **A** = [3 -6], **B** = [2 -1 3] [1 3], [4 6 -2] determine the: - **(a)** order of AB. - **(b)** matrix BA, if it exists. - **(c)** determinant of A. ### 6. Given that **A** = [2 1 2], **B** = [1 -1], **C** = [2 1 -2], [-1 3], [-1 -3], [ 2 1 2], calculate: - **(a)** B + AC - **(b)** the values of x and y, if BC = [x+y -4] [-1 -3 -3] ### 7. Evaluate A² + 2A - 3I for A = [0 1 0] and I is an identity matrix of multiplication. [0 0 3] [1 0 0] ## Tutorial 6.0 ## Topic: Matrix Operations and Determinant of Square Matrices (Answers) ### 1. - **A**: 4 x 2 - **B**: 2 x 4 - **C**: 4 x 1 - **D**: 4 x 3 ### 2. - **(a)** [5 3] [7 2] - **(b)** [-19 -4] [1 -8] - **(c)** [10 24] [14 32] ### 3. - **(a)** -2 - **(b)** -16 ### 4. -16 ### 5. - **(a)** 3 x 1 - **(b)** does not exist - **(c)** 0 ### 6. - **(a)** [4 2 4] [0 -2 1] [0 0 0] - **(b)** x = 2, y = 4 ### 7. [0 5 7] [0 0 12] [1 0 0]