设A为m×n矩阵，且

证明方程组AX=b有且仅有n-r+1个线性无关解；

Samuel is a partner in a firm of wholesale food distributors. There are two other partners, Arthur and Dhondy. The partnership is registered and the partnership deed provides that all three partners must consent to any contract in excess of R50,000.Samuel entered into three contracts in the partnership’s name, each of which is valued at more than R50,000, without consulting with his other two partners. The three contracts relate to the purchase of:(a) a consignment of tinned fruits;(b) office equipment; and(c) an expensive car.Required:Advise Arthur and Dhondy whether the partnership is liable on these contracts. (10 marks)