[理工] 線代

[lxy351 (kklin)]

 Find the determinant of the n*n matrix
          ┌                                          ┐
          │  a+b  ab    0    0   …   0    0    0    │
          │   1   a+b  ab    0   …   0    0    0    │
          │   0    1   a+b  ab   …   0    0    0    │
   A =    │   …   …   …  …   …   …   …   …   │
          │   0    0    0    0   …   1   a+b   ab   │
          │   0    0    0    0   …   0    1    a+b  │
          └                                          ┘

Let T and U be linear transformations with standard matrices A and
   (A^T)A, respectively. Let T be onto.
(a) Show whether U is onto, on-to-one, or invertible.
(b) What is the dimension of the null space of U? Explain your answer.


這二題不知道怎麼下手~ 麻煩各位高手幫忙  謝謝

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