Linear Algebra Answers

a. Find the orthogonal and normal canonical forms of 2y^2-2yz+2zx-2xy.

b. The operation,* defined by a*b= sin(ab), is a binary operation on N

True or false with full explanation

Suppose that A, B, C are 3×3 matrices with det (A) = 2, det (B) = 3 and det (C) = 5. Compute the following determinants:

(a) det (AB)

(b) det (3AB^-2C²)

(c) det (A²C^TB^-1)

The sum of three numbers is 20. If we multiply the first number by 2 and add the second

number and subtract the third number, then we get 23. If we multiply the first number by 3

and add second and third number to it, then we get 46. Let x be the first number, y be the

second number and z

be the third number.

(a) Obtain a system of linear equations to represent the given information.

(b) Write down the system in (a) as a matrix equation.

(c) Use inverse matrix to solve for x , y and z .

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