HW1: Linear Algebra Review
All problems need to be solved by hand calculation with clear steps. Calculators and/or computers
cannot be used for these matrix operations. They can only be used for scalar number operations.
Given Matrices A, B and C.
𝐴=[4 3 1
3 3 2
3 4 5] 𝐵=[−1 3 −2
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2 −6 4] 𝐶 = [1 4 2 −3
6 5 0 −7
8 2 1 3
0 5 3 4]
(1) Find AB and BA.
(2) Find the determinant and the inverse of A.
(3) Find the determinant and the inverse of B.
(4) Find the determinant and the inverse of C.
Show your work with all the major steps such as dot products for the matrix multiplication, the
cofactors, the cofactor matrix and the adjoint matrix.
