Linear Algebra Answers

A curve

y  ax  bx  c

2

where a, b and c are constants, passes

through the points (2,11), (-1,-16) and (3,28).

(a) By using the above information, construct a system

containing three linear equations.

(b) Express the above system as a matrix equation

AX  B.

(c) Find the inverse of matrix A by using the adjoint matrix

method. Hence, obtain the values of a, b and c.

A curve

y  ax  bx  c

2

where a, b and c are constants, passes

through the points (2,11), (-1,-16) and (3,28).

an assignment is worth 300 points. for each day the assignment is late, the professor deduct 2 points from the assignment grade. write a linear function that represents the maximum number of points the assignment may receive at a given time, assuming it was turned in after it was due

T : R

3 → R

2

 defined by : 9 

T(x, y, z) = (x -y + z, -2x + 2y -2 z)

Using matrix method, solve the simultaneous equations

{x-3y=3

5x-9y=11

consider matrix A=[101 212 313 111] find the nullity and rank

consider the subspace of W={a,b,a+b)|a,b ER}. Basis for W is, write out te definition for W^T and find a basi B for W^T

let A be a 7*5 matrix with rank(A)=2 complete dim(row space of A) , dim( column space of A) ,dim (null space of A) and (null space of A^t)

Let T:U→V be a linear transformation. Let 0_u and 0_v be zero vectors of U and V. Show that T(0_U )=0_V