Julesange
Matrix Operations
2x2 Matrix
3x3 Matrices
Solving Systems of Linear Equations
100
Det var midt en julenat. Julemanden skreg: Jeg kan ikke finde vej..
Hvad er 'Kender I den om Rudolf'
100
A = (-1 0 1 5) B = (3 4 -1 -2) C = (4 -1 -1 3) Find (A +B) + C
What is (6 3 -1 6)
100
Find the inverse matrix of (2 4 -1 5).
What is 1/14(5 -4 1 2)
100
Find the determinant of A. A = (1 2 4 2 0 1 3 -1 2)
What is -9?
100
Solve the system x - y - z = 2 x + y + 3z = 7 9x - y - 3z = -1
What is x = 0.6, y = -5.3, z = 3.9.
200
Determine the order of (5 1 0 2).
What is 1x4?
200
Explain why it is true that if X + A = B then X = B - A.
What is if X + A = B then X + A + (-A) = B + (-A) therefore X + 0 = B - A therefore X = B - A
200
Find the inverse matrix of (2 4 1 2)
What is the inverse doesn't exist?
200
Find the determinant. (2 3 0 -1 2 1 2 0 5)
What is 3?
200
Write the following matrix as a matrix equation: a + b - c = 7 a - b + c = 6 2a + b - 3c = -2
What is (1 1 -1 multiplied by (a equals (7 1 -1 1 b 6 2 1 -3) c) 2)
300
A grocery list consist of 2 loaves of bread, 1 kg of butter, 6 eggs and 1 carton of cream. The cost of each grocery item is $1.95, $2.35, $0.15 and $0.95 respectively. What is the significance of (2x1.95) + (1x2.35) + (6x0.15)+ (1x 0.95)?
What is the total cost of the groceries?
300
A = (1 3 5) C = (1 0 2 3 1 4) Find AC.
What is (12 29)?
300
If A = (4 k find A^-1 and state the values of k for 2 -1) which this inverse exists.
What is 1/-4-2k(-1 -k what is when k doesn't equal 2. -2 4)
300
Find k given that the determinant of the following matrix = 0. (k 2 1 2 k 2 1 2 1).
What is 4 or 1?
300
Solve the system of equations 4a + 7b - 3c = -8 -a - 2b + c = 3 6a + 12b - 5c = 15
What is a = 2, b = -1, c = 3?
400
Big Bart's Baked Beans factory produces cans of baked beans in 3 sizes: 200g, 300g, and 500g. In February they produced respectively: 1000, 1500, and 1250 cans of each in week 1; 1500, 1000, and 1000 of each in week 2; 800, 2300, and 1300 cans of each in week 3; 1200 cans of each in week 4. Construct a matrix to show February's production levels.
What is (1000 1500 1250 1500 1000 1000 800 2300 1300 1200 1200 1200)
400
If A = (1 2 find A^2. 3 4 5 6)
What is A^2 doesn't exist?
400
Consider the system 2x - 3y = 8 4x - y = 11. Write the equations in the form AX = B.
What is (2 -3 (x (8 4 -1) multiplied by y) equals 11).
400
Use technology to find the inverse of A. (3 2 3 1 -1 2 2 1 3)
What is (5/4 3/4 -7/4 -1/4 -3/4 3/4 -3/4 -1/4 5/4)
400
Using technology, solve 10x - y + 4z = -9 7x + 3y - 5z = 89 13x - 17y + 23z = -309
What is x = 3, y = 11, and z = -7?
500
Over a long weekend holiday, a baker produced the following food items: On Friday he baked 40 dozen pies, 50 dozen pastries, 55 dozen rolls, and 40 dozen buns. On Saturday, 25 dozen pies, 65 dozen pastries, 30 dozen buns, and 44 dozen rolls were made. On Sunday, 40 dozen pastries, 40 dozen rolls, and 35 dozen of each of pies and buns were made. On Monday the totals were 40 dozen pastries, 50 dozen buns, and 35 dozen of each of pies and rolls. Represent this information in a matrix.
What is (40 50 55 40 25 65 44 30 35 40 40 35 35 40 35 50)
500
Give one example which shows the statement "if A^2 = 0 then A = 0" is false.
What is A = (0 1 0 0) and A ^2 = (0 0 0 0)
500
If A^2 = 2A + 3I, find A^-1 in the linear form rA + sI, where r and s are scalars.
What is A^-1 = 1/3A - 2/3I?
500
Find the product of the following matrices. (2 0 3 and (-11 9 15 1 5 2 -1 1 1 1 -3 1) 8 -6 -10). Hence find the inverse of (2 0 3 1 5 2 1 -3 1)
What is (2 0 0 0 2 0 0 0 2) and what is (-11/2 9/2 15/2 -1/2 1/2 1/2 4 -3 -5)
500
Rent-a-car has three different makes of vehicles, P, Q and R, for hire. These cars are located at yards A and B on either side of a city. Some cars are out (being rented). In total they have 150 cars. At yard A they have 20% of P, 40% of Q and 30% of R, which is 46 cars in total. At yard B they have 40% of P, 20% of Q and 50% of R, which is 54 cars in total. How many of each car type does Rent-a-car have?
What is 45 of P, 55 of Q and 50 of R?
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