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a. Fill in the blank in the following statement: "If A is an m X n matrix, then the columns of A are linearly independent if and only if A has pivot columns."
b. Explain why the statement in (a) is true.
The sum of the cubes of three consecutive positive integers is always a multiple of 9. Factorize x2n +1 - 1 as a product of real linear and quadratic polynomials.
The length of a rectangle is increasing at a rate of 2 ft. per second, while the width is increasing at a rate of 1 ft. per second. When the length is 4 ft. and the width is 5 ft., how fast, in square feet per second, is the area increasing?
the transamerica pyramid in san francisco is 853 ft tall with a squre base that is 149 ft on each side. what is the volume to the nearest thousand cubic foot?
Of the first 90 customers, 44 selected chicken, 23 selected roast beef, 13 select steak, and 10 selected fish. Should the manager revise his estimates? Use = 0.01.
The number of moose in northern Maine is increasing at a rate of 3% per year. It is estimated in one county that there are now 2000 moose. If the growth rate remains unchanged, how many years will it be until there are 2600 moose in that county?
trade discount of 30 and 10 are to be taken on an invoice that totals 2546.45 including prepaid shipping charges of
What two variables have the strongest positive strength of relationship?
What is the shape of the cable that supports the roadway of a suspension bridge? Our model is based on the following simplifying instructions
A plane is heading due south with an airspeed of 229 mph. A wind from a direction of 52 degrees is blowing at 13 mph. Find the direction the plane is actually headed. (Note that bearings are measured from north, clockwise.
What are the possible numbers of minutes he has used his phone in a month?Use m for the number of minutes, and solve your inequality for m.
For each exercise, specify whether it involves an arithmetic sequence or a geometric sequence and use the proper formulas where applicable.
A ball re-bounds one-half the height from which it is dropped. The ball is dropped from a height of 160 feet and keeps bouncing. What is the total vertical distance the ball will travel from the moment it is dropped until it hits the floor for the..
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