Addition and Subtraction of a Matrix

Q. 20. A cubic polynomial p(x) such thatp(1)=1, p(2)=2, p(3)=3, p(4)=5, then the value of p(6) is equal to

Q. 30. Let a, b, c and k be real numbers and p(x) be the polynomial (x-a) (x-b) (x-c) + x. If p(k)=k , then the sum of all possible values of k is what?

Q.

Factorise:

2x²+7x+3

Q.

Let p and q are distinct naturals such that 2005+p=q² and 2005+q=p².Find the value of 2014+pq

Q. 47 If p(x)=ax3-bx2-3x+18 is divided by x+1 and x+2 then the remainder are 12 and -20 respectively. The values of a and b are respectively ?

Q.

If 3X + 2Y = I and 2X - Y = O, where I and O are unit and null matrices of order 3 respectively, then

1. $X=\left(\frac{2}{7}\right),Y=\left(\frac{1}{7}\right)I$

2. $X=\left(\frac{2}{7}\right)I,Y=\left(\frac{1}{7}\right)I$

3. $X=\left(\frac{1}{7}\right)I,Y=\left(\frac{2}{7}\right)$

4. $X=\left(\frac{1}{7}\right)I,Y=\left(\frac{2}{7}\right)I$

Q. If $x-\frac{1}{x}=3+2\sqrt{2}$, find the value of $x^3-\frac{1}{x^3}$

Q.

Do determinants multiply?

Q.

If A = $\left[\begin{array}{cc}0& 2\\ 3& 5\end{array}\right]$, B = $\left[\begin{array}{ccc}3& 4& 5\\ 2& 3& 1\\ 1& 3& 7\end{array}\right]$ then A + B =

1. 

2. 

3. None

4. 

Q.

In each of the first six problems, take p(x) as the first polynomial, q(x) as the second polynomial and compute the following.

p(1) q(1); p(0) q(0); p(1) q(−1); p(−1) q(1)

Q.

Find X if $2X+3Y=\left[\begin{array}{cc}2& 3\\ 4& 0\end{array}\right]and3X+2Y=\left[\begin{array}{cc}7& -2\\ -1& 5\end{array}\right]$

1. $\left[\begin{array}{cc}\frac{-2}{5}& \frac{-13}{5}\\ \frac{-14}{5}& 2\end{array}\right]$

2. $\left[\begin{array}{cc}\frac{-2}{5}& \frac{12}{5}\\ \frac{11}{5}& -3\end{array}\right]$

3. $\left[\begin{array}{cc}\frac{2}{5}& \frac{-12}{5}\\ \frac{-11}{5}& 3\end{array}\right]$

4. $\left[\begin{array}{cc}\frac{2}{5}& \frac{13}{5}\\ \frac{14}{5}& -2\end{array}\right]$

Q.

If A = $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ and B = $\left[\begin{array}{ccc}4& 5& 6\\ 7& 8& 9\\ 1& 2& 3\end{array}\right]$ then the order of A+B will be nxn where n= -----

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Q.

If x+1 x = 5 , then evaluate x⁴ +1 x⁴

Q.

If A = $\left[\begin{array}{ccc}2& 4& 8\\ 6& 9& 1\\ 8& 7& 5\end{array}\right]$ and B = $\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\\ 7& 8& 9\end{array}\right]$ then the third element of the first row of A - B = -------

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Q. factors of square root 3 x² +11x + 6 square root of 3

Q. Find the value of a and b if :3 +root 2 upon 3-root 2 =a+b root 2

Q. What can be the general notation of a matrix with 4 rows and 5 columns?

1. 5x4
2. 4x5
3. 4x4
4. 5x5

Q. Evaluate using formula: 7³ +3³ +(-10³)

Q. 1/2+root 3 +2/root5-root3 +1/2- root 5=0

Q. Solve:
$\frac{x-3}{x^2+4}\ge \frac{5}{x^2+4}$

1. $x\ge 8$
2. $x=8$
3. $x\le 8$
4. none

Q.

find the value of x³ + 1/ x³ , when x +1/x =15