a) Let A be a 2 × 2 matrix. Show that for ALL choices of scalars a, that if A = aI2, then AB = BA for ALL 2 × 2 matrices B.   b) For ALL 2×2 matrices A where A is NOT a scalar multiple of I2, find a 2 × 2 matrix C with AC ̸= CA (Hint: use matrices with a single nonzero entry.)

Q: What is the perimeter of a rectangle with length x and width x-5

A: To find the perimeter of a rectangle whose length is x and width is x-5.

Q: Exercise 5 questions B and/or C

A: Refer to the question, in mathematical induction first prove that the equation holds for n=1.Then we...

Q: Give a rule of the piece wise define funsten give the domain and the range

A: Definition:A piecewise defined function is a function defined by at least two equations ("pieces"), ...

Q: Algebraically find the age of the tree when the height of the cherry tree is 24 feet Y=5.81+6.20lnX

A: Given:Height of the cherry tree is 24 feet:

Q: A 120. MW coal plant wants to add a SOx emissions control system to reduce its emissions. The emissi...

A: Consider the given information:

Q: A medical insurance service reports that health-care expenditures per capita were $2823 in 1990 and ...

A: (a) Since x is the number of years after 1990, the value of x = 0 in 1990 and the expenditure in 199...

Q: factor 12x^3 +71x^2 +102x +40

A: To factor the given expression, find out possible root and use synthetic division to factor it. Appl...

Q: Find x- and y- intercepts of: 2x+4y+8=0

A: Consider the given equation:

Q: Can someone help me solve this problem? Number 16

A: Given

Q: Simplify  4a2-b2/ab/2a+b/a

A:

Q: Factoring the diffrence of two squares. A. x2-9

A: First express 9 as a square. 9=3^2 Plug 9=3^2 in the given expression.

Q: Traveling against the current, it takes a boat h hours to go m miles. Traveling with the current, th...

A: Let x miles per hour be the speed of boat in still water and let c miles per hour be the speed of cu...

Q: Use slope intercept form to write the equation of the line with the given properties. Write each equ...

A: Formula:

Q: It takes 20 cubic feet of concrete make a 80 square foot patio. How many cubic yards of concrete doe...

A: Given,20 cubic feet of concrete make 80 square foot patio.

Q: Fill in the blank with the greatest digit that makes the statement true 9|505_1

A: If a number is divisible by 9 then the sum of its digits should also be divisible by 9.

Q: Simplify completely  4x+12/5X2+19x+12

A: The given expression is,

Q: Find the slope-intercept form of the line that satisfies the given conditions. Through A(−7, 5) and...

A: The slope intercept form of the line is given by,y = mx + cWhere, m is the slope and c is the y-inte...

Q: How would the graphs of   y=log(x8) and   y=8⋅log(x) compare?

A: Here we have to compare graphs of y = log(8x) and y = 8log(x)To compare the above given graphs let u...

Q: Solve the equation 6/5y - 1/6= 1/2 (3y-1)

A: To solve the given equation.

Q: SCIENCE Amug of hot chocolate is 90°C at timet = 0. It is surrounded by air at a constant temperatur...

A: The temperature of a mug after t minute is given by

Q: Can someone help me solve this problem? Number twelve

A: The given equation is

Q: One zero of the polynomial is given. Use it to express the polynomial as a product of linear and irr...

A: Given:

Q: Solve the equation    y-8/5+2=2/5-y/3

A: Given:

Q: An amount of P dollars is borrowed for the given length of time at an annual interest rate of r. Fin...

A: To find the simple interestThe provided information is as followsAmount of dollars, P = $2200Rate of...

Q: Please solve equation in the attachment.

A: Given information:

Q: (-3.7,15.3) and (-3.2,14.4)  what is the slope. Simplify answer please

A: To determine the slope of line.

Q: (a) The total surface area of Asia is approximately 17,200,000 square miles. Write this number in sc...

A: (a) The total surface area of Asia is approximately17,200,000 square miles. Write this number in sci...

Q: Scientific notation is a common way of writing very large numbers. In everyday life we see this when...

A: Part first:Given that phone has a free storage of 10 GB (gigabytes).Convert 10 GB into Bytes,

Q: A (6,−7) B (2,3)Step 1 of 2 : Plot the given points on the graph. AnswerTo plot a point on the graph...

A: To sketch the point (6,–7), first move 6 units from origin in the x-axis right side and then move 7 ...

Q: Find the present value of the ordinary annuity. (Round your answer to the nearest cent.) $1400/semia...

A: We know that,

Q: what are the blanks

A: According to the given information the given functions are:

Q: Using the model N(a), algebraically determine how much money needs to be spent on advertising in ord...

A: Given model is, 

Q: In the expression below, a is an integer.  12x2 + ax -20  If 3x +4 is a factor of the expression abo...

A: 3x+4 is a factor so by factor theorem ,3x+4=0x= -4/3 is a zero of the equation.

Q: 3. Find the percentage of data points that lie between z1 picture to support your = -3.01 and z2 = 2...

A: Find the percentage of data points that lies between z1=-3.01 and z2=2.61. Find the graph for it?

Q: I'm confused on how to put a piecewise function into interval notation

A: To rewrite the definition of the given function using interval notation

Q: The slope is 2/5 and the line passes through the point (-5,4).

A:

Q: (Z over 8) - (1 over 2) = (z over 6)

A: Given equation is 

Q: Determine whether the ordered pair is a solution of the system of equations. (5, 1) x + y = 6 3...

A: Given equation

Q: A carpenter purchased 70 ft of redwood and 90 ft of pine for a total cost of $353. A second purchase...

A: Let x and y denotes the cost of the redwood per feet and the cost of the pine per feet, respectively...

Q: 9. Using your calculator or Excel find the line of best fit (regression line) for the data given in ...

A: Open ti-graphing calculator and press ON button. 

Q: One grade of tea, worth $3.90 per pound, is to be mixed with another grade worth $2 per pound to mak...

A: Given information:

Q: Find the domain and the vertical and horizontal asymptotes 5 f(x) 22 Domain: Vertical asymptote(s): ...

A: The function is given by,

Q: Use point slope form to write the equation of the line passing through the two given points. Write e...

A: 19) We know that slope of line joining two points (x1,y1), (x2,y2) is (y2-y1)/(x2-x1). Therefore, sl...

Q: Find the domain of the indicated combined function. 38) Find the domain of (fg)(x) when f(x) 3x4 and...

A: Given, 

Q: The equation y=36+18x models the relationship between the height y, In inches, of a typical golden d...

A: In y=36+18x , y=height and x=number of years (Given)

Q: (1-3x)/4)=(x+6/3)+1/2

A: LCM of 4,3,2 is = 12We multiply both side by 12 and distribute.

Q: Will someone help me with this problem?  Sub parts d,e,f

A: (d) y-intercept is the point on graph at which it intersects the y-axis.

Q: A motorboat traveling with the current went 140 mi in 5 h. Traveling against the current, it took 7 ...

A: To determine the speed of current and speed of boat.

Q: There is one value of x for which the equation  y = (3)/(x-5)  has no ordered-pair solution. What is...

A: To determine the value of x, for which equation has no ordered pair.

Q: 2x2-x=-2

A: Assuming that the given equation needs to be solved, the solution is given below :

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.