Linear Algebra Answers

A company that manufactures cars used three different types of steels S1, S2, and S3 for producing three cars C1, C2, and C3. The tons of steel requirement in each type of car is given in below table Cars Steel C1 C2 C3 S1 1 1 1 S2 1 2 4 S3 4 2 3 Determine the number of cars of each type which can be produced using 45, 120 and 130 tones of steel of the three types respectively. (Hint: use gaussian method)

write the list for the SBN:A={x:xs greater than or equal to -3, x is an element of the set of integers}

Two of the eigenvalues of a 3*3 matrix A are 2 and 3 and the determinant is 48. Find the third eigenvalue and the trace (A)

Given that matrix A has 1has the eigenvalue with the corresponding eigenvector (1,-3) and 5 as the second eigenvalue with (1,1) as the corresponding eigenvector. (I) find the matrix A (Ii) D the diagonal matrix such that P^-1 AP=D

Let a, b, c, d be a set of real numbers, show that a²+b²+c²+d²=1

If the matrix of

a²-1 ab ac ad

ba b²-1 bc bc

ca cb c²-1 cd

da db dc d²-1

equal to zero.

Let a, b, c, d be a set of real numbers, show that a²+b²+c²+d²=1

If the matrix

a²-1 ab ac ad

ba b²-1 bc bc

ca cb c²-1 cd

da db dc d²-1

equal to zero.

Let V=R. Define addition and scalar multiplication by a+b=4a+4b. Show whether addition is both commutative and associative.

If dim V

T be a linear transformation on V and A and B be two ordered bases for V and A is the matrix of T relative to A and B is the matrix of T relative to B then prove that A and B are similar.

If T and S are similar then prove that T^(2) and S^(2) are also similar .Further if T and S are invertible then prove that T^(-1) and S^(-1) are also similar.