EXAMPLE 5: FINDING THE SUM AND DIFFERENCE OF TWO 3 X 3 MATRICES

Given $A$ and B

Find the sum.
Find the difference.

errorA=\left[\begin{array}{rrr}\qquad 2& \qquad -10& \qquad -2\\ \qquad 14& \qquad 12& \qquad 10\\ \qquad 4& \qquad -2& \qquad 2\end{array}\right]\text{ and }B=\left[\begin{array}{rrr}\qquad 6& \qquad 10& \qquad -2\\ \qquad 0& \qquad -12& \qquad -4\\ \qquad -5& \qquad 2& \qquad -2\end{array}\right]

B = ⎣ ⎡ 60 - 5 10 - 12 2 - 2 - 4 - 2 ⎦ ⎤

Expert Solution

Solution

Add the corresponding entries.

$\begin{array}{l}\qquad \\ A+B=\left[\begin{array}{rrr}\qquad 2& \qquad -10& \qquad -2\\ \qquad 14& \qquad 12& \qquad 10\\ \qquad 4& \qquad -2& \qquad 2\end{array}\right]+\left[\begin{array}{rrr}\qquad 6& \qquad 10& \qquad -2\\ \qquad 0& \qquad -12& \qquad -4\\ \qquad -5& \qquad 2& \qquad -2\end{array}\right]\qquad \\ =\left[\begin{array}{rrr}\qquad 2+6& \qquad -10+10& \qquad -2 - 2\\ \qquad 14+0& \qquad 12 - 12& \qquad 10 - 4\\ \qquad 4 - 5& \qquad -2+2& \qquad 2 - 2\end{array}\right]\qquad \\ =\left[\begin{array}{rrr}\qquad 8& \qquad 0& \qquad -4\\ \qquad 14& \qquad 0& \qquad 6\\ \qquad -1& \qquad 0& \qquad 0\end{array}\right]\qquad \end{array}$
Subtract the corresponding entries.

$\begin{array}{l}\qquad \\ A-B=\left[\begin{array}{rrr}\qquad 2& \qquad -10& \qquad -2\\ \qquad 14& \qquad 12& \qquad 10\\ \qquad 4& \qquad -2& \qquad 2\end{array}\right]-\left[\begin{array}{rrr}\qquad 6& \qquad 10& \qquad -2\\ \qquad 0& \qquad -12& \qquad -4\\ \qquad -5& \qquad 2& \qquad -2\end{array}\right]\qquad \\ =\left[\begin{array}{rrr}\qquad 2 - 6& \qquad -10 - 10& \qquad -2+2\\ \qquad 14 - 0& \qquad 12+12& \qquad 10+4\\ \qquad 4+5& \qquad -2 - 2& \qquad 2+2\end{array}\right]\qquad \\ =\left[\begin{array}{rrr}\qquad -4& \qquad -20& \qquad 0\\ \qquad 14& \qquad 24& \qquad 14\\ \qquad 9& \qquad -4& \qquad 4\end{array}\right]\qquad \end{array}$

SUN BUNRA answered 2 years ago

1) Write an algorithm to calculate the sum of the following series: Sum =x-x3/3! + x5/5!...

1) Write an algorithm to calculate the sum of the following series: Sum =x-x3/3! + x5/5! – x7/7! +……. Stop when the term<0.0001. 2) An internet service provider charges its subscribers per month as follows: Data usage (n), in gbs charges (NIS) 0.0<n<=1.0 250 1.0<n<=2.0 500 2.0<n<=5.0 1000 5.0<n<=10.0 1500 n>10 2000 Write a C program to read the usage(n) from a file and print the charges to be paid by the subscribers. Your program must include the function calculate...

Write a C++ program to determine the sum of two 1-D matrices: A = [a b...

Write a C++ program to determine the sum of two 1-D matrices: A = [a b c d] B = [e f g h] The user will provide the values of a to h.

Which of the following are true? (1) The sum of two invertible matrices is invertible (2)...

Which of the following are true? (1) The sum of two invertible matrices is invertible (2) The determinant of the sum is the sum of the determinants (3) The determinant of the inverse is the reciprocal of the determinant (4) An nxn matrix is invertible if and only if its determinant is zero (5) The product of two invertible matrices is invertible (so long as the product is defined) (6) If A is a diagonal 3x3 matrix [a,0,0;0,b,0;0,0,c] then its...

In C++ Exercise #3: Develop a program (name it AddMatrices) that adds two matrices. The matrices...

*****In C++***** Exercise #3: Develop a program (name it AddMatrices) that adds two matrices. The matrices must of the same size. The program defines method Addition() that takes two two-dimensional arrays of integers and returns their addition as a two-dimensional array. The program main method defines two 3-by-3 arrays of type integer. The method prompts the user to initialize the arrays. Then it calls method Addition(). Finally, it prints out the array retuned by method Addition(). Document your code, and...

Approximate the area under the curve y=x^3+4 from x=2 to x=5 using a left sum with...

Approximate the area under the curve y=x^3+4 from x=2 to x=5 using a left sum with 6 subdivisions. The area is approximately

f(x,y) = x^3+y^3-18xy Finding relative max and mins.

What is the difference between multiplying a matrix times a vector and multiplying two matrices?

3. Suppose that a divide and conquer algorithm for multiplication of n x n matrices is...

3. Suppose that a divide and conquer algorithm for multiplication of n x n matrices is found such that it requires 6 multiplications and 31 additions of n/2 x n/2 submatrices. Write the recurrence for the running time T(n) of this algorithm and find the order of T(n).

What is the difference in finding magnitude of a force on a charge and finding the...

What is the difference in finding magnitude of a force on a charge and finding the net electric force acting on a charge? If given three charges set at a certain places set on a triangle, how would you find the magnitude of a force on one of the charges? Please create a simple example and show each step clearly and explanation for what to do in each step esecially on how to find, set up, and use the components...

Finding the complexity of Finding the largest two elements in a queue of size n+3 using...

Finding the complexity of Finding the largest two elements in a queue of size n+3 using Naïve search. with explain

Question