(a) Find general solutions of AX=0. (10 points)

【已刪除】七、 A metal container 0.6 m high, with an inside cross-sectional area of 0.09 m2, has a mass of 2.5 kg when empty. The container is placed on a scalc and water flows in llirough an opening in the top and out through the two equal area openings in ihc sides, as shown in the diagram. Under steady conditions, the height of Ihc water in llic tank is 0.57 m. Dclcrminc ihc reading on Ihc scalc. The density of water is 1000 kg/m3. (20%)

【已刪除】12.淡疆保險公司隨機抽出1200位大學生，並針對他們對人壽保險商品的偏好的做問卷調查，並得出如下的偏好列聯表  試在α = 0.05的顯著水準下，檢定大學生對人壽保險商品的偏好，是否存在性別差異? (11%)

【已刪除】1. Let A=  • Find det(A). (10 points) 

2. LetT: R3 → R2 be a linear transformation and T(l，0，0)=(l，-2)，T(l,l,0)=(l,3), T(0,0，l)=(2，-1). Find T(x，y，z). (10 points)

(b) Find Rank(A). (5points)

【已刪除】4. Let P=. Show that P is invertible and find   p-1 .(10 points)

5. Let T : P2 → R2 be deflned by T(a+bx+cx2) = (a-b,c+a) and B={1, x,x2}，D={(1,-1)，(0，1)}. Find the matrix of T corresponding to the ordered bases B and D. (10 points)

6. Suppose that {x, y} is a linearly independent set in a vector space V. Show that if T : V -＞ W is a" one -to-one linear transformation, then {T(x+2y), T(2x-y)} is also linearly independent. (10 points)

(a) Find the characteristic polynomial of A. (5points)

(b) Find an invertible matrix P such that p-1 AP is diagonal. (10 points)