Singular matrix
A singular matrix is a square matrix that does not have an inverse. In mathematical terms, a matrix is said to be singular if its determinant is equal to zero. This condition implies that the _____ _____ ________ __________ ________ _____ _____ _________ ________ ______ _______ ________.
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An individual consumer consumes two commodities X₁ & X₂. The utility function is
The price of commodity one is P₁ = Rs.3.00, the price of commodity two is P₂ = Rs.4.00, the individual's income per period is Rs.108. Determine the utility maximizing level of X₁ & X₂ and derive the demand curves for the two commodities.
Decomposable matrix
Let Z = f(x,y) = 3x³-5y²- 225x + 70y + 23.
(i) Find the stationary points of z.
(ii) Determine if at these points the function is at a relative maximum, relative minimum, infixion point, or saddle point.
Let the production function by . Find the elasticity of production with respect to labour (L).
Solve the following differential equation
given Y(0) = 4
5. If Z = f(x,y) = xy
Find the maximum value for f(x,y) if x and y are constrained to sum to 1 (That is, x+y = 1). Solve the problem in two ways: by substitution and by using the Lagrangian multiplier method.
Explain the concept of maximum value function.
Consider the following two matrices
A =
B =
(i) Find the rank of 'A' and 'B'
(ii) Show that (AB)⁻¹ = B⁻¹ A⁻¹
(iii) Show that (A⁻¹)⁻¹ = A
(iv) Show that (B⁻¹)⁻¹ = B