Linear Algebra Answers

Express the following as a linear combination of

p1 = 3 + x + 2x2, p2 = 5 - x + 5x2, and p3 = 2 + 5x + 3x2.

Let

1) a11 x1 + a12 x2 + a13 x3 = b1
2) a21 x1 + a22 x 2+ a23 x3 = b2
3) a31 x1 + a32 x 2+ a33 x 3 = b3

SHOW that if det(A) does not equal 0, where det (A) is the determinant of the coefficient matrix, then x2= det(A2)/det(A)

where det (A2) is the determinant obtained by replacing the second column of det (A) by (b1, b2, b3) to the power T.

Please assist.

LET A and B be any two matrices such that B in the inverse of A.

1) Determine the relationship between the adjoint of A and the adjoint of B (5 MARKS)

2) Determine the relationship between the transpose of A and the transpose of B (5 marks).

Please assist.

Solve the given matrix using strassen’s matrix multiplication
A matrix is 3 5
5 8
B matrix is 8 9
4 7

Find a c-inverse of the matrix
A D
2
4
1 0
2

Find the entries xi;i D 1; 2; 3; 4 in the matrix P so that P is an orthogonal matrix where
P D
1
2
2
6
6
4
1 1 1 1
1 1

[img]https://upload.cc/i1/2020/04/06/lcgHuW.jpg[/img]


question is in photo, R=4

let T:P2-->P2 defined by T(a+bx+cx^2)=(2b+3cx+(a-b)x^2) check T is linear trnsfrmtn.find matrix wrt bases B={x2,x2+x,x2+x+1} ,B2={1,x,x2}.find kernel of T

A car rental company owns five types of cars: Small,Economy, Standard, Family, Exclusive. The prices for per day rent for eachtype of the cars are given in British pounds by the1×5matrix

Suppose u and v are nonzero vectors in 3-space, where u=(u1, u2, u3) and v=(v1, v2, v3). Prove that u x v is perpendicular to both u and v by making use of the dot product.