t 21. Suppose the last column of AB is entirely zero but B itself has no column of zeros. What can you say about the columns of A?
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- Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X BEquation does have x in it. Other.PERFECT CUBES AND SQUARES PROBLEMSThe product of some integer with itself is called a perfect square. A perfect cube isthe result of multiplying an integer three times by itself. Assume that a perfectcube greater than 2000 is considered a large perfect cube, the ones between 500and 2000 (inclusive) are medium perfect cubes and the ones below 500 are smallprefect cubes. A perfect cube is associated with a perfect square if the sameinteger is either cubed or squared i.e. the perfect square 4 (2x2) is associated withthe perfect cube 8 (2x2x2)Write a program which:1. Asks the user to enter a perfect square.2. Finds the associate perfect cube.3. Determines whether the found perfect cube is small, medium or large.4. Informs the user if the input is not a perfect square.5. Ask the user is they would like to continue or not. Use a while loop to dothis.For example,Example 1:Enter perfect square: 36216 is a small perfect cubeContinue (Y/N): YEnter perfect square: 4008000 is a large perfect…
- True or False 1. Matrices are often represented by single small letters a, b, c... etc.2. Two m x n matrices A and B are equal if aij=bij for each i & j. (i.e., the two matrices havesame size, and all the corresponding elements are equal).3. Matrices A & B are said to be conformable in the order AB if, and only if, the number ofrows in A is equal to the number of columns in B.4. Suppose Matrix A is having 4 rows and 3 columns, and Matrix B is having 3 rows and 2columns. The product size of AB is a 4 x 2 matrix.5. Suppose B is the matrix obtained from an n x n matrix A by multiplying the entries in arow/column by a non-zero constant and adding the result to the corresponding entries inanother row/column. Then, det(B) = det(A).Determine whether the statement below is true or false. Justify the answer. A general solution of a system is an explicit description of all solutions of the system. Choose the correct answer below. A. The statement is false. Each different choice of a free variable produces the same solution of the system. B. The statement is true. After applying the row reduction algorithm and generating a general solution of a system, the rightmost column displays all of the particular solutions of that system. C. The statement is false. A general solution is the result of an inconsistent system, which has no particular solution. D. The statement is true. The row reduction algorithm leads directly to an explicit description of the solution set of a linear system when the algorithm is applied to the augmented matrix of the system, leading to a general solution of a system.Find how many positive integers with exactly four decimal digits, that is, positive integers between 1000 and 9999 inclusive, have the following properties: (a) are divisible by 5 but not by 7. (b) are divisible by 5. (c) have distinct digits. (d) are divisible by 5 or by 7 (inclusive or).
- 7. The roots of the quadratic equation ax² + bx + c = 0, a 0 are given by the following formula: -b = √b² - 4ac 2a In this formula, the term b² - 4ac is called the discriminant. If b²-4ac0, then the equation has a single (repeated) root. If 200The fuel economy of a car is the distance which it can travel on one litre of fuel. The base fuel economy (i.e., its fuel economy when there is only one person - the driver - in the car) of a certain car is MM kilometres per litre. It was also observed that every extra passenger in the car decreases the fuel economy by 11 kilometre per litre. PP people want to take this car for a journey. They know that the car currently has VV litres of fuel in its tank. What is the maximum distance this car can travel under the given conditions, assuming that all PP people always stay in the car and no refuelling can be done? Note that among the PP people is also a driver, i.e., there are exactly PP people in the car. Solve in any programming languageSuppose that the equation ax b .mod n/ is solvable (that is, d j b, whered D gcd.a; n/) and that x0 is any solution to this equation. Then, this equation has exactly d distinct solutions, modulo n, given by xi D x0 C i.n=d / fori D 0; 1; : : : ; d 1