计算题 证明：秩等于r的对称矩阵可以表成r个秩等于1的对称矩阵之和.

x21+x22+x23+x24+2x1x2+2x2x3+2x3x4.

问答题x²₁+x²₂+x²₃+x²₄+2x₁x₂+2x₂x₃+2x₃x₄.

x21+2x22+x24+4x1x2+4x1x3+2x1x4+2x2x3+2x2x4+2x3x4.

问答题x²₁+2x²₂+x²₄+4x₁x₂+4x₁x₃+2x₁x₄+2x₂x₃+2x₂x₄+2x₃x₄.

x1x2+x1x3+x1x4+x2x3+x2x4+x3x4.

问答题x₁x₂+x₁x₃+x₁x₄+x₂x₃+x₂x₄+x₃x₄.