Ask question

Ask question

All categories

3 years ago

7

A general 2x2 diagonal matrix has the form(a00b). Thus the two unknown real numbers a b are needed to specify each 2x2 diagonal

matrix. In Exercises 11 16, how many unknown real numbers are needed to specify each of the given matrices
1. An upper triangular 2x2 matrix?
2.) An m × n matrix?

1 answer:

horsena [70]3 years ago

6 0

Answer:

1. 3, and 2. m x n

Step-by-step explanation:

1. for an upper triangular 2x2 matrix i.e. (a,0,c,d), three (03) unknown elements a, c, and d are needed to be specified.

2. for m x n matrix, m*n elements are needed to be specified.

You might be interested in

I dont know how to make 0.3 as a fraction and then simplify.

Lapatulllka [165]

0.3 is 3/10, (which is already simplified) because .3 is out of 1. Which means that that 1 is 10. Which is 3/10.

7 0

3 years ago

Read 2 more answers

2/7m-1/7=3/14 solve step by step

yulyashka [42]

Solution for $\frac{2}{7}m - \frac{1}{7} = \frac{3}{14} \ is \ m = \frac{5}{4} \ or \ m = 1\frac{1}{4} \ or \ m = 1.25$

<h3>Further explanation</h3>

It is a case about one variable linear quations and we have to solve the equation to get the variable m. There are two ways to solve it!

Our main plan is to isolate the variable m alone at the end of the process on one side of the equation until the variable will be equal to the value on the opposite side.

<u>First way</u>

$\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}$

Let us add $\frac{1}{7}$ to both sides

$\frac{2}{7}m - \frac{1}{7} + \frac{1}{7} = \frac{3}{14} + \frac{1}{7}$

$\frac{2}{7}m = \frac{3}{14} + \frac{1}{7}$

On the right side for the addition operation, we equate the common denominator by multiplying $\ \frac{1}{7} \ by \ \frac{2}{2}$

$\frac{2}{7}m = \frac{3}{14} + \frac{2}{14}$

Then we combine terms to get

$\frac{2}{7}m = \frac{5}{14}$

Divide by the coefficient of m, or in other words, multiply both sides by $\frac{7}{2}$

$\frac{2}{7}m \times \frac{7}{2} = \frac{5}{14} \times \frac{7}{2}$

Finally, the solution is obtained as follows

$m = \frac{35}{28}$

Simplify fractions, both the numerator and denominator are divided equally by 7.

$\boxed{ \ m = \frac{5}{4} \ }$

Convert into mixed fractions, we get:

$\boxed{ \ m = 1 \frac{1}{4} \ }$

In decimal form, we get

$m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }$

<u>Second way (a quick way)</u>

$\frac{2}{7}m - \frac{1}{7} = \frac{3}{14}$

Because the denominators 7 and 14 have LCM = 14, both sides are multiplied by 14 (LCM is the Least Common Multiple)

$14 \times \big( \frac{2}{7}m - \frac{1}{7} \big) = 14\times \big( \frac{3}{14} \big)$

We use the distributive property of multiplication on the left side

$\frac{28}{7}m - \frac{14}{7} = \frac{42}{14}$

or it can also directly lead to

$4m - 2 = 3$

Add 2 to both sides, we get

$4m = 5$

Divide by the coefficient of m, or in other words, both sides are divided by 4

$\boxed{ \ m = \frac{5}{4} \ }$

Or, $\boxed{ \ m = 1 \frac{1}{4} \ }$

Or, $m = 1 \frac{25}{100} \rightarrow \boxed{ \ m = 1.25 \ }$

Wanna check the solution into the equation?

$\big( \frac{2}{7} \times \frac{5}{4} \big) - \frac{1}{7} = \frac{3}{14}$

$\frac{10}{28} - \frac{1}{7} = \frac{3}{14}$

$\frac{5}{14} - \frac{2}{14} = \frac{3}{14}$

$\frac{3}{14} = \frac{3}{14}$

Both sides show the same value, so the solution is correct.

Note:

Remember, how to manipulate both sides of the equation with the algebraic properties of equality such as:

adding,
subtracting,
multiplying, and/or
dividing both sides of the equation with the same number.

In the form of fractions, the steps that must be considered are

equate the denominator,
simplify fractions, and
for the final answer, convert fractions to mixed fractions or decimal forms

All these processes can occur repeatedly until the isolated variables are obtained on one side of the equation.

<h3>Learn more</h3>

A word problem that forms a single variable linear equation brainly.com/question/1566971
Learn more about the single variable linear equation that has no solution, has one solution, and has infinitely many solutions brainly.com/question/2595790
Questioning the stages of solving a word problem about one variable linear equations brainly.com/question/2038876

<h3>Answer details </h3>

Grade : Middle School

Subject : Mathematics

Chapter : Linear Equation in One Variable

Keywords : solve, solution, variable, coefficient, 2/7m - 1/7 = 3/14, 5/4, 1 1/4, 1.125, algebraic properties of equality, one, linear equation, isolated, manipulate, operations, add, subtract, multiply, divide, fraction, equate, denominator, numerator, both sides, decimal

4 0

3 years ago

Read 2 more answers

A container shapes like an inverted cone holds 96 cubic centimeters of water. The height of the cup is 14 centimeters. Find the

Korolek [52]

Answer:

Cone Volume = (PI * radius^2 * height) / 3

96 cc = (PI * radius^2 * 14) / 3

(96 * 3) / (PI * 14) = radius^2

radius ^ 2 = 6.5480890872

radius = 2.5589234235

diameter = radius *2 = 5.117846847 cm

diameter = 5.12 cm (rounded)

Step-by-step explanation:

5 0

2 years ago

I need help with the bottom one the absolute value one

astra-53 [7]

Absolute value is simply the non-negative version of the number regardless of its symbol

So for the absolute value of 20? the answer is just 20.

For reference, the absolute value of -20 is also just 20.

Hope the explanation helps :)

5 0

3 years ago

Read 2 more answers

Convert 110 km/myr (kilometers per million years) to cm/yr (centimeters per year)

jenyasd209 [6]

Answer:

$110\ \text{km/myr} =11\ \text{cm/yr}$

Step-by-step explanation:

To find : Convert 110 km/myr (kilometers per million years) to cm/yr (centimeters per year) ?

Solution :

Using metric conversions,

1 kilometer = 1000 meter

1 meter = 100 centimeter

So, 1 kilometer = 100,000 centimeter

and 1 million year = 1,000,000 year

$1\ \text{km/myr} =\frac{100000}{1000000}\ \text{cm/yr}$

$1\ \text{km/myr} =0.1\ \text{cm/yr}$

So, $110\ \text{km/myr} =110\times 0.1\ \text{cm/yr}$

$110\ \text{km/myr} =11\ \text{cm/yr}$

Therefore, $110\ \text{km/myr} =11\ \text{cm/yr}$

6 0

3 years ago

Read 2 more answers