# Linear Models-Use of G-Inverse (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 1 - 1 of 1

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## Question number: 1

» Linear Models » Use of G-Inverse

Appeared in Year: 2014

### Describe in Detail

Obtain a g-inverse of A given below and verify that AA ^{-} A = A

### Explanation

Let A be a full rank m n matrix. By full rank we mean rank (A) = min {m, n}.

If m < n, then A has a right inverse given by

If m > n, then A has a left inverse given by

Our matrix A is 2 × 3 with rank two, so A has a right inverse given by

Putting A ^{-} = then gives

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