Matrices & Determinants Questions and Answers
Math
Matrices & DeterminantsCostumes have been designed for the school musical. Costume A requires 5 yards of fabric, 4 yards of ribbon, and 3 packets of sequins. Costume B requires 7 yards of fabric, 4 yards of ribbon, and 1 packet of sequins.
Fabric costs $5 per yard, ribbon costs $3 per yard, and sequins cost $1.50 per packet.
Use matrix multiplication to find the total cost of the materials for each costume.
Math
Matrices & DeterminantsFor what value(s) of k will the following system of linear equations have no solution? infinitely many solutions?
x-3y = 5
- 6x + 18y = k
...
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
OA. The given system has no solution for all real numbers k except for k=
(Use a comma to separate answers as needed.)
OB. The given system has no solution for all real numbers k.
OC. The given system has a solution for all real values k.
Math
Matrices & DeterminantsMark each statement True or False. Justify each answer.
a. A row replacement operation does not affect the determinant of a matrix.
b. The determinant of A is the product of the pivots in any echelon form U of A, multiplied by (-1)^r, where r is the number of row interchanges made during row reduction from A to U.
c. If the columns of A are linearly dependent, then det A = 0.
d. det(A + B) = det A + det B.
Math
Matrices & DeterminantsSolve each system analytically. If the equations are dependent, write the solutions set in terms of the variable z.
3x+6y-z = 6
2x-3y + 5z = -10
8x+9y-2z= 12
Math
Matrices & DeterminantsSolve the system analytically. If the equations are dependent, write the solution set in terms of the variable z.
x+y+z= -2
2x+y-z = -14
x-y+z= -4
Select the correct choice below and, if necessary, fill in any answer boxes to complete your choice.
A. There is one solution. The solution set is .
B. The system has infinitely many solutions. The solution set is ..., where z is any real number.
C. The solution set is Ø.
Math
Matrices & DeterminantsIf the column space of a 3x3 matrix consists of all vectors b=[b₁ b2 b3] such that b₁+ b2= 3b3 then
one of the following set of the vectors forms abasis for the left null space of that matrix:
[113] and [11-3]
[11-3]
[331] and [33-1]
[33-1]
Math
Matrices & Determinants(10 points) Write the augmented matrix from the system of equa-
tions. Then, solve the system using Gaussian elimination (elementary
row operations).
x - 3y + 2z = 12
2x5y + 5z = 14
x - 2y + 3z =
20
Math
Matrices & DeterminantsWrite a matrix equation equivalent to the following system.
2x - 3y = -1
4x + 5y = 9
Find the inverse of the coefficient matrix, and use it to solve the system.
Math
Matrices & DeterminantsIn the vector space P2, of polynomials of degree at most two, the third column of the matrix of
from the transition basis
B={e₁=4-x², e ₂ = −2 + 3x², e3=1+x} to the basis A={a₁=1, a₂=x, a3=x²} is:
Math
Matrices & DeterminantsUse Gauss-Jordan row reduction to solve the given system of equations. HINT [See Examples 1-6.] (If there is no solution, enter NO SOLUTION. If the system is dependent,
express your answer in terms of z, where = x(z) and y = y(z).)
8x - y + z = 2
9x - y + z = 5
(x, y, z) =
Math
Matrices & DeterminantsWrite the following system of equations as a matrix equation and solve the system by finding the inverse of the coefficient matrix.
|3x-y+2z=-1
|4x-2y+z=-7
|-x+3y-2z=-1
Math
Matrices & DeterminantsIf A is an invertible square matrix of order less than 4 such that |A-AT|!=0 and B = adjA, then which of the following is/are always true -
adj(B²A-¹B-¹A) = A
adj(B²A-¹B-¹A) = B
Order of A is 2
Order of A is 3
Math
Matrices & DeterminantsProve that any Möbius transformation can be written in a form with determinant 1, and that this form is unique up to sign.
How does the determinant of T(z) = (az+b)/(cz + d) change if we multiply top and bottom of the map by some constant k?