1、高等代数与解析几何英文习题高等代数与解析几何英文习题1. (Feb. 28) Is a basis for the linear space of all matrices?2. (Mar. 1)Let . Find vectors and that are both orthogonal to and to each other.3. (Mar. 4)Let be a basis for a linear space and let be a subspace of . Is it necessarily true that a basis for is a subset of ? Why?
2、4. (Mar. 7)In (1)-(2) determine which of the given functions are inner products on where and (1) ;(2) .5. (Mar. 8) In Exercises (1)-(2) determine whether the given set of vectors is orthogonal, orthonormal, or neither with respect to the Euclidean inner product. (1) ; (2) .6. (Mar. 11) Compute the a
3、rea of the triangle with vertices , , and .7. (Mar. 14) Show that .8. (Mar. 15) In Exercises (1) and (2) find an equation for the plane that passes through the point and that is parallel to the plane whose general equation is given.(1) ; .(2) ; .9. (Mar. 18) Let : be a linear transformation such tha
4、t(a) Find ;(b) Find ;(c) Find a matrix such that.10. (Mar. 21) If spans a linear space , is it possible for to span ? Explain your answer.11. (Mar. 22)In Exercises (1) and (2) find parametric equations for the line of intersection between the planes whose general equations are given.(1) ; .(2) ; .12
5、. (Mar. 25)In Exercises (1)-(2) name the surface determined by the given equation and give its equation in a coordinate system in which the surface is in standard position.(1) .(2) 13. (Mar. 28)In Exercises (1)-(2) find the matrix representation of the given linear transformation : with respect to the ordered bases for and for .(1) .(2) .14. (Mar. 29)In Exercises (1)-(2) find bases for the kernel and range of the given linear transformation : .(1) .(2) .4 / 4
