Perform the indicated matrix operations:

$\left[\begin{array}{cc}5& 4\\ -3& 7\\ 0& 1\end{array}\right]-\left[\begin{array}{cc}-4& 8\\ 6& 0\\ -5& 3\end{array}\right]$

SchachtN
2021-03-09
Answered

Perform the indicated matrix operations:

$\left[\begin{array}{cc}5& 4\\ -3& 7\\ 0& 1\end{array}\right]-\left[\begin{array}{cc}-4& 8\\ 6& 0\\ -5& 3\end{array}\right]$

You can still ask an expert for help

2k1enyvp

Answered 2021-03-10
Author has **94** answers

Step 1

According to he question,, we have to subtract the given two matrix$\left[\begin{array}{cc}5& 4\\ -3& 7\\ 0& 1\end{array}\right]-\left[\begin{array}{cc}-4& 8\\ 6& 0\\ -5& 3\end{array}\right]$ .

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.

We can perform the operations like addition or subtraction with the corresponding elements and solve accordingly.

Step 2

Rewrite the given matrices,

$\left[\begin{array}{cc}5& 4\\ -3& 7\\ 0& 1\end{array}\right]-\left[\begin{array}{cc}-4& 8\\ 6& 0\\ -5& 3\end{array}\right]$

Now subtract the corresponding elements,so,

$\left[\begin{array}{cc}5& 4\\ -3& 7\\ 0& 1\end{array}\right]-\left[\begin{array}{cc}-4& 8\\ 6& 0\\ -5& 3\end{array}\right]=\left[\begin{array}{cc}5+4& 4-8\\ -3-6& 7-0\\ 0+5& 1-3\end{array}\right]$

$=\left[\begin{array}{cc}9& -4\\ -9& 7\\ 5& -2\end{array}\right]$

Hence, the value of the matrices$\left[\begin{array}{cc}5& 4\\ -3& 7\\ 0& 1\end{array}\right]-\left[\begin{array}{cc}-4& 8\\ 6& 0\\ -5& 3\end{array}\right]$ is $\left[\begin{array}{cc}9& -4\\ -9& 7\\ 5& -2\end{array}\right]$

According to he question,, we have to subtract the given two matrix

Matrix, a set of numbers arranged in rows and columns so as to form a rectangular array. The numbers are called the elements, or entries, of the matrix.

We can perform the operations like addition or subtraction with the corresponding elements and solve accordingly.

Step 2

Rewrite the given matrices,

Now subtract the corresponding elements,so,

Hence, the value of the matrices

Jeffrey Jordon

Answered 2022-01-24
Author has **2313** answers

Answer is given below (on video)

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Let B be a 4x4 matrix to which we apply the following operations:

1. double column 1,

2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

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2. halve row 3,

3. add row 3 to row 1,

4. interchange columns 1 and 4,

5. subtract row 2 from each of the other rows,

6. replace column 4 by column 3,

7. delete column 1 (column dimension is reduced by 1).

(a) Write the result as a product of eight matrices.

(b) Write it again as a product of ABC (same B) of three matrices.

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Can someone explain why I get wrong answer in simplifying this expression?

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If we rewrite the expression with new angles,

$\frac{29\pi}{12}\to \frac{5\pi}{12}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\frac{13\pi}{12}\to \frac{11\pi}{12}$

we don't change the value of the expression. But, if we now use sine of sum of angles, we get $\frac{1}{2}$ instead of 0.

Why does this happen? Do angles need to be in the same quadrant for the formula to work?

$\mathrm{sin}\frac{11\pi}{12}\mathrm{sin}\frac{29\pi}{12}-\mathrm{cos}\frac{13\pi}{12}\mathrm{cos}\frac{41\pi}{12}$

If we rewrite the expression with new angles,

$\frac{29\pi}{12}\to \frac{5\pi}{12}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\frac{13\pi}{12}\to \frac{11\pi}{12}$

we don't change the value of the expression. But, if we now use sine of sum of angles, we get $\frac{1}{2}$ instead of 0.

Why does this happen? Do angles need to be in the same quadrant for the formula to work?

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Evaluate the determinant of each of the following matrices:

a.$\left[\begin{array}{cc}10& 9\\ 6& 5\end{array}\right]$

b.$\left[\begin{array}{cc}4& 3\\ -5& -8\end{array}\right]$

a.

b.

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