Q-2: a) Consider the linear system 3x + y 2z = 8 4x-z = -1 (2x-3y+5z = -32 ' (i) Solve the linear system. (ii) Find the inverse of the coefficient matrix. b) For what values of h, vector u = (h,-3,-5) can be written as a linear combination of the vectors v₁ = (1,0,-2), and v₂ = (-2,1,7).

Q: Use deductive reasoning to prove that if you pick any number n, subtract 18 from the number,…

A: The question is based on simple deductive reasoning

Q: How many six-digit even numbers are possible if the leftmost digit cannot be​ zero?

A: From the given information,Sample space = {0,1,2,3,4,5,6,7,8,9}It has been given that the leftmost…

Q: How many zeros does 25! end with?

A: A number will have trailing zeros when 5 and at least one even number are factors of it.   Also, the…

Q: 14 Solve 5 140 40 60 45 50

A: Given The given expression is 145=140x.

Q: What number has a remainder of 2 when divided by 3, a remainder of 3 when divided by 5 and a…

A:

Q: how many positive integers less than 150 with a remainder of 3 if divided by 7?

A: To find number of positive integers less than 150 with a a remainder of 3 if divided by 7

Q: The ten's digit in a two-digit number is 2 greater than the one's digit. If we interchange the…

A: Topic- Linear equations We are given The ten's digit ina two digit number is 32 greater than the…

Q: How many 7 digit phone number are possible? Assume the first digit can be zero and all digits can be…

A: make 7 digit phone number.The first number can be zero and all digits can repeated. The digits are :…

Q: list the first five multiples of 13 after 13 itself.

A:

Q: How many 5 digit odd numbers can you make if the digits 0-4 are available and each digit may only be…

A: Combination of the muber

Q: In a two-digit number, the tens-digit is greater than the units-digit. The product of these two…

A:

Q: How many three digit numbers have the property that the sum of that number and the three digit…

A: How many three digit numbers have the property that the sum of that number and the three digit…

Q: The formula N= 3x² + 5x + 1 represents the number of households N, in thousands (i.e. if the number…

A:

Q: A number is divisible by 2 if

A: A number is divisible by 2 if

Q: If the largest of 89 consecutive integers is 327, what is the smallest?

A: It is given that largest to the 89 consecutive integers is 327. We need to find the smallest integer…

Q: Can a number N, sum of whose digits is 21345, be a square of a natural number?

A: Given: a number N, sum of digit is 21345

Q: The product of an even number and any other number is even.

A: The product of an even number and any other number is even.

Q: How many integers must you pick in order to be sure that at last two of them have the same remainder…

A: To Find: Number of integers that must be picked in order to be sure that at least two of them have…

Q: A prime number that is a common factor of 20 and 32 ?

A: Consider the given positive integer 20 and 32.In order to find the prime factor of 20 and 32, first…

Q: Solve step by step in digital format 6.- A championship is organized between 10 athletes to select…

A: Given data : Total number of athletes = 10 3 = Athletes will represent the country in the World cup.…

Q: Find the smallest number greater than 200 with 14 positive divisors

A:

Q: Any n consecutive integers will include a number that is divisible by n.

A:

Q: How many five-letter words that have at least two consecutive letters are the same (the number of…

A: Given : Number of letter  word =5 total alphabests letter =26number of consecutive same = at least 2…

Q: When an integer n is divided by 6, the remainder is 5. What are the possible values of the remainder…

A: From the statement, we can say that

Q: how many 6 digit numbers can be formed, if at the place of hundred thousand there are allowed two…

A: Yes your step is right.Hundredth thousand place can be chosen in 2 ways. And hundredth place can be…

Q: If the largest of 89 consecutive integers is 327, what is the smallest?

A:

Q: How many squares are there in a 6x6 magic square?

A: Answer is 91.

Q: How many nine-digit numbers with twice as many odd digits as even digits? (leading zeros are…

A: The number of digits are 9. The number of odd digits are twice the number of even digit.

Q: How many two digits number divisible by 3 ?

A:

Q: How many four-digit even numbers are possible if the leftmost digit cannot be​ zero?

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…