Linear Algebra Answers

Solve the following national income models by Cramer’s rule Y=C+I+1000,C=10+0.7(Y-T),I=100+0.2Y,T=0.3Y Where Y , C , I, M and T are national income, consumption, investment imports and taxes.

Western Air sold twenty-seven airline tickets to Cape Town on a certain day. Each Economy class ticket (E) was sold at N$3200 and the First-class tickets (F) were sold at N$4100 each. The total amount received for the twenty-seven tickets was N$92700.

4.5.1 Formulate the above information into two linear equations [2]

4.5.2 Solve these equations simultaneously using the substitution method and calculate the number of first-class tickets sold. [6]

Let A = \(\\mathrm{\\{}\)1,2\(\\mathrm{\\}}\), B = \(\\mathrm{\\{}\)a,b,c\(\\mathrm{\\}}\), C = \(\\mathrm{\\{}\)c,d\(\\mathrm{\\}}\). Find \(A\\ \\times\\ (B\\cap\\ C). \)

a.\\(\\left[\\begin{array}{cc} 1 & 0\\\\ 0 & 1 \\end{array}\\right]\\)

b.\\(\\left[\\begin{array}{cc} 1 & 1\\\\ 1 & 1 \\end{array}\\right]\\)

c.\\(\\left[\\begin{array}{cc} -1 & 1\\\\ 1 & -1 \\end{array}\\right]\\)

d.\\(\\left[\\begin{array}{cc} 0 & 1\\\\ 1 & 0 \\end{array}\\right]\\)

A) Suppose A is a 3 x 3 matrix such that det (A) = 1/125 . Find det (5A^-1)



B)Suppose A is a 3 x 3 matrix such that det (A) = 5. Determine det [A^4]

A) Suppose A is a 3 x 3 matrix such that det (A) = 1/125 . Find det (5A^-1)



B)Suppose A is a 3 x 3 matrix such that det (A) = 5. Determine det [A^4]

Let the plane V be defined by ax + by + cz + d = 0 with at least one of a; b or c different from zero

and d >= 0.

Then the distance between V and the origin is d/(a^2+b^2+c^2)^1/2 : Prove this statement.

Explain the difference between a singular and a non-singular matrix. Show that a non-singular

matrix must be square.

Let A be a 3 x 3 matrix A with eigenvalues

1, –2, 2. Find the trace of A + A². Give

reasons to justify your answer.

Let W {(x, y, z) R3: x + y + z = 0}. Check

if W is a subspace of R3 . Find a non-zero

subspace U of R3 so that W intersection U = (0).

Check if (1, 3, 0) lies in the range of a linear

operator T on R3 given by

T (x1, x2 , x3) = (x1 , x2+ x3, x1– x2).

Is T one-one and onto ? Give reasons.