Matrix | Tensor Analysis Answers

How to find a matix when its inverse and determinant are provided?

if the value of a 3*3 determinant is 3, then the value of the determinant formed by its co factors will be-
a)9
b)3
c)27
d)none of these

What is a Tensor?

explain tensor. prove that the sum of two tensor is a tensor. show that by contraction , the rank of tensor is reduced by two.

1.Show that the set V of real valued functions defined on [0,1] with addition defined as (f+g)(x)=f(x)+g(x) and scalar multiplication(αf)(x) =αf(x)for α£R,is a vector space over R
2.Find the parametric equation and symmetric equations for the line though the points (5,3,1)&(2,1,1)
3.let V=R3 and
Determinate whether
W1={(a,b,c)}:c>0}.
W2={(a,b,c):a2+b2<=0.}
4.sho that S={(1,1,3),(0,-1,2),(1,0,1)}is a basis for R3
5.find a unit vector whose direction is opposite to the vector i-3j -5k
6.given (1 0 0,0 1/2 0 ,0 0 -1/3)A(1 1,1 2)=(1 0,0 1,0 0)find A
7.find the value of X A=[ 1 1 0,1 0 -1,1 2 x] is invertible .in that case give A-1

8.show that S={(1,1),(-1,2)}is a generator of R2
9.is (3,2,2)a linear combination of (a)(0,1,1),(2,0,0),(1,0,0)?(b)(1,0,0)(2,2,1)
10,let u and V be vectors with π/3the angle b/n them ,if//u//=2and //V//=3then find U.V and U.U
11.find the inverse of the matrix A=(-1 3 7 5,-1 2 -1 3,2 0 1 4,1 -1 -1 3) if possible

inverse the matrix(2 0 1,3 2 -5,1 -1 0) by gauss jordan method

A buffet sells plates for seniors at $6, adults at $9, and children for free. If 150 plates were purchased for total receipts of $960 and twice as many adult plates were purchased as senior plates, how many of each type of plate were sold? 1)This problem can be solved using a system of equations. Identify the variables to be used in the system. 2)Write one equation to represent the total number of plates sold.3) Write one equation to represent the total receipts.4) Describe how a third equation can be written. What is that equation?5) Use a system of equations to solve the problem.

matrix[6,2,-3_0,-4,5]
- matrix[4,-1,2_-5,1,-2]
Any help on this will be appreciated...must show work

20. Use an inverse matrix to solve the following system of equations.
x + y – 2z = 0
x – 2y + z = 0
x – y - z = -1

Use an inverse matrix to solve the following system of equations.
2x – y = -3
2x + y = 7