Prove that the rows/columns of a skew-symmetric matrix a of odd order are linearly dependent.
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Problem 564
Let A and B be n×n skew-symmetric matrices. Namely AT=−A and BT=−B.
(a) Prove that A+B is skew-symmetric.
(b) Prove that cA is skew-symmetric for any scalar c.
(c) Let P be an m×n matrix. Prove that PTAP is skew-symmetric.
(d) Suppose that A is real skew-symmetric. Prove that iA is an Hermitian matrix.
(e) Prove that if AB=−BA, then AB is a skew-symmetric matrix.
(f) Let v be an n-dimensional column vecotor. Prove that vTAv=0.
(g) Suppose that A is a real skew-symmetric matrix and A2v=0 for some vector v∈Rn. Then prove that Av=0.
please tick the brainliest answer.
Problem 564
Let A and B be n×n skew-symmetric matrices. Namely AT=−A and BT=−B.
(a) Prove that A+B is skew-symmetric.
(b) Prove that cA is skew-symmetric for any scalar c.
(c) Let P be an m×n matrix. Prove that PTAP is skew-symmetric.
(d) Suppose that A is real skew-symmetric. Prove that iA is an Hermitian matrix.
(e) Prove that if AB=−BA, then AB is a skew-symmetric matrix.
(f) Let v be an n-dimensional column vecotor. Prove that vTAv=0.
(g) Suppose that A is a real skew-symmetric matrix and A2v=0 for some vector v∈Rn. Then prove that Av=0.
please tick the brainliest answer.
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