## 1. Define the following matrices

 m1 = 3×4 matrix of zeroes m2 = the 3×3 matrix where row1=(1,2,0), row2=(2,5,-1), row3=(4,10,-1) m3 = transpose of m2 m4 = matrix product of m2 and m3 m5 = sum of m2 and m3 m6 = elementwise product of m2 and m3 m7 = matrix inverse of m2 m8 = the 5×5 identity matrix

 ``` m1 = Table[0, {3},{4}] m2 = { {1,2,0}, {2,5,-1}, {4,10,-1} } m3 = Transpose[m2] m4 = m2 . m3 m5 = m2 + m3 m6 = m2 * m3 m7 = Inverse[m2] m8 = IdentityMatrix[5] ```

## 2: Eigenvalues, Eigenvectors, SVD

Perform these essential matrix functions on matrix M:
 M   = ``` 5.2 3.0 -4.1 -3.9```

e = eigenvalues of M
v = eigenvectors of M
SVD of M
(singular value decomposition)
 ``` m = { {5.2,3.0}, {-4.1,-3.9} } e = Eigenvalues[m] v = Eigenvectors[m] SingularValues[m] ```

## 3: Solve matrix equation Ax=b

Solve Ax=b (and check the solution) given that

 A = ```1 2 0 2 5 -1 4 10 -1 ``` b = ```7 8 9 ```

 ``` A = { {1,2,0}, {2,5,-1}, {4,10,-1} } b = {7,8,9} x = LinearSolve[ A, b ] A . x (* yes, it does equal b *) ```