Read \'Least Squares\' before attempting this problem. Let M be an m times n mat

Question

Read 'Least Squares' before attempting this problem. Let M be an m times n matrix and let V be a vector in R^m. Decide whether each of the following statements is true or false. The matrix M^T M must be a square matrix. The equation MX = V must have a solution. That is, there must be some vector X such that MX = V. If X_0 is some vector in R^n such that MX_0 = V, then X = X_0 must be a least-squares solution to MX = V. If x_0 is some vector in R^n so that times = X_0 is a least-squares solution to MX = V, then it must also be true that MX_0 = V.

Explanation / Answer

1.True

If M be an m*n matrix

MT be an n*m mtrix

Therefore MTM be an (n*m * m*n ) m*m matrix.which means it is suqare matrix.

2.False

If MX=V then X can be any value, X can be a constant.

3. True

4.True

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