Linear Algebra Questions, HELP PLZ?
I will write [[a,b],[c,d],[e,f]] for the 3x2 matrix with first row entries a, b, and second row entries c, d, and third row entries e, f. The possible 3x2 rref's are: the zero matrix, [[0,1],[0,0],[0,0]], [[1,0],[0,0],[0,0]], and [[1,0],[0,1],[0,0]]. There aren't any others. Why? Well, a 3x2 matrix in rref either has 0, 1, or 2 pivots. If it has 0 pivots it's the Zero matrix. If it has 1 pivot, either it's in the first column or the second column of the first row, and that gives us the next two in my list. If it has two pivots, it has to be the fourth matrix on my list. So whatever your list of five matrices is, check the one that isn't one of those four and convince yourself it isn't in rref after all. (Does it have more than one nonzero entry in a single column? Then it isn't in rref. Does it have a nonzero row below a zero row? Then it isn't in rref. Do the pivots not move from left to right as you move down the rows? Then it isn't in rref.) I would solve the second problem by row reducing the 4x3 augmented matrix corresponding to this system, which is A = [[1,1,0,1],[0,1,-1,3],[1,0,1,k]]. Apply the following row operation to A: (1) replace row 3 by the result of subtracting row 1 from row 3. The result is the matrix A' = [[1,1,0,1],[0,1,-1,3],[0,-1,1,k-1]]. apply the following row operation to A': (2) replace row 3 by the result of adding row 2 to row 3. The result is the matrix A'' = [[1,1,0,1],[0,1,-1,3],[0,0,0,k+2]]. If k+2 is nonzero, this is the matrix of an inconsistent system (since the augmented matrix of a consistent system cannot have a pivot in the last column when it is put in row echelon form, and if k+2 is nonzero, we can divide the third row by it and get a matrix in row echelon form with a pivot in the last column). If k+2 is zero, then this is the matrix of a consistent system. So the condition for consistency is k+2 = 0, which is solved when k = -2. I hope this helped!
ALGEBRA LINEAR EQUATIONS! HELP!?
Please answers these or at least give me some help i only need 2 inequalities with which to graph. I need them by 8 o'clock tonight. #1 You arrive late to class for an unexcused reason, and only have 45 minutes to complete your math exam. The exam has to complex word problem questions and 30 easier multiple choice questions. Each correct word problem is worth 20 points and each correct multiple choice question is worth 2 points. You know that it usually takes you 15 minutes to answer a word problem question and only one minute to answer a multiple choice question. Assume that for each question you answer, you receive full credit. How many of each type of question should you answer to receive the maximum possible points? What is the maximum possible points that you can earn in the 45 minutes? #2 A landscape contractor uses a combination of two brands of fertilizers, each containing different amounts of phosphates and nitrates, as shown in the table below. A certain lawn requires a mixture of at least 24 lbs of phosphates and at least 16 lbs of of nitrates Graph (I tried my best): Phosphate content per package Nitrate Content Per P Brand A 4 lbs 2 lbs Brand B 6 lbs 5 lbs If a package of Brand A costs $6.99 and a package of Brand B costs $17.99, find the lowest cost needed to produce this mixture. Please guys help me! i just need 2 inequalities for both. I have been stewing it over all day and i cant figure it out. Please Help!
Are these algebra questions about a linear equation correct please help?
Are these Algebra problems correct if not please explain them. Thank you If the graph of a system of linear equations shows three lines such that two lines coincide with each other, and the third is parallel to the first two, how many solutions does the system have? =0 solutions Which is the value of z in the system of equations below? x+y+z=-1 -2x-y+z=-10 x-2y-z=0 =value of z is 0
Algebra 2 question (linear equations) word problem?
Linear equations take the form y = a + bx, where a is a constant (called the y intercept), and b is the slope of the line. The constant in this case is the cost of the parts, or $105. The slope is the hourly rate, or $25/hour. A clue here is that slope will usually be reported in terms of y/x or a rate, while the constant is usually just in terms of y. So... y = $105 + $25/hr(x) Since we know the total amount is $180, that is our y value, now solve the equation for x 180 = 105 + 25x 180 - 105 = 25x 75 = 25x 75/25 = x 3 = x
What is the correct answer to the following linear algebra question?
Q: Give an example of an inconsistent underdetermined system of two equations in three unknowns. My answer: All underdetermined systems are inconsistent. I thought the number of equations must be equal to or greater than the number of unknown variables in order for a linear system to have a solution set. What is your opinion? What is the correct answer?
ALGEBRA - LINEAR EQUATIONS HELP!! 10 Points!!!?
1. Write the slope-intercept form of the equation of the line through the given points. through: (3,4) and (5,-2) I also didn't get... 2. Write the slope-intercept form of the equation of the line described. a. through: (1,-5), parallel to y = 1/4x - 4 b. through: (1,4), perp. to y = - 1/5x - 3 I'm sorry if this is a lot to ask but Thank you to whoever helps me I have a test tommarow and I was sick from school today to ask my teacher Thank You
Is this correct? Algebra 2. Arithmetic and geometrie equations? And help? Please? :)?
1. Suppose your business made a profit of $5500 the first year. If the profit increases 20% per year, find the total profit over the first 5 years. My answer= 40,928.8, I did it the long way. 2. A seashell has chambers that are each 0.82 times the length of the next chamber is 32mm around. Find the total length of the shell's spiraled chambers. 3. A 20-row theater has two aisles. The two side sections have 2 chairs in the first row and one more chair in each succeeding row. Find the total seating capacity of the theater. How would I solve these? Please help these are the last 3 of my study guide and I'll be well off for the test tomorrow. Thank you all for the help! :)
Algebra 2- Solving systems of linear equations in 3 variables?? HELP?
In the above EX addequation 2 to equation 1 generating 6y + 4 z = -6 = EQ A Then multiply the 3rd equation by 3 and add to second equation -5y + 17 z= -56 = EQ B then multiply EQ A by 5 and EQB by 6 and add them you get 122Z = -366 so z = -3 now subsstitute -3 for z in equation 1 and equation 2 getting 3x + 2y + 3 = 8 -3x + 4y -15 = 14 ad theses 2 equations 6 y - 12 = -6 6 y = 6 y = 1 now substitute the value of z and y into any of the three equations nd solve for X....X = 1 so X=1, Y =1 Z=-3 your turn....