Search & Filtering
Suppose U1,U2,..,Um are finite-dimensional subspace of V.
Prove that :
U1+U2+...+Um is finite dementional and
dim(U1+U2+...+Um)≤ dimU1 + dimU2 + ..... + dimUm
Assume that T is an n×n matrix with a row of zeros .Prove that T has no inverse
Suppose v1,v2, vm is linearly independent in V and w ∈ V . Prove that dim span(v+w,v2+w,..vm+w)≥ m-1
The population of South Africa (in millions) was 52 million in 2011 and 56.2 million in 2016.
Assume that the relationship between the
y
and the year
t
is linear. Let
t = 0
represent 2011.
1.1.1 Write a linear model for the data. What is the slope and what it tells you
about the population?
Prove that if A is a square matrix then AA^T and A + A are symmetric
Consider the following augmented matrix [ 1 -1 2 1]
[3 -1 5 -2]
[-4 2 x^2-8 x+2]
Determine the values of x for which the system has
I) no solution,
Ii) exactly one solution,
Iii) infinitely many solutions
Use the cofactor expansion to determine
{{2000}{3120}{2-504}{1303}}
Use Cramer’s rule to solve for y without solving for x, z and w in the system 2w + x + y + z = 3 −8w − 7x − 3y + 5z = −3 w + 4x + y + z = 6 w + 3x + 7y − z = 1
Write notes on how to add, subtract and multiply matrices, and show how they may apply to solving a three system of equation , site examples on the applications of matrices to solving real world business problems
Assume that T is an n x n matrix with a row of zeros. Prove that T has no inverse.
