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3 years ago

If two matrices, A and B, are equal, which of the

Mathematics

2 answers:

alexandr402 [8]3 years ago

8 0

If A and B are equal:

Matrix A must be a diagonal matrix: FALSE.

We only know that A and B are equal, so they can both be non-diagonal matrices. Here's a counterexample:

$A=B=\left[\begin{array}{cc}1&2\\4&5\\7&8\end{array}\right]$

Both matrices must be square: FALSE.

We only know that A and B are equal, so they can both be non-square matrices. The previous counterexample still works

Both matrices must be the same size: TRUE

If A and B are equal, they are literally the same matrix. So, in particular, they also share the size.

For any value of i, j; aij = bij: TRUE

Assuming that there was a small typo in the question, this is also true: two matrices are equal if the correspondent entries are the same.

Digiron [165]3 years ago

8 0

Both matrices must be square

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Joanna set a goal to drink more water daily. The number of ounces of water she drank each of the last seven days is shown below.

DaniilM [7]

(a) Data with the eight day's measurement.

Raw data: [60,58,64,64,68,50,57,82],

Sorted data: [50,57,58,60,64,64,68,82]

Sample size = 8 (even)

mean = 62.875

median = (60+64)/2 = 62

1st quartile = (57+58)/2 = 57.5

3rd quartile = (64+68)/2 = 66

IQR = 66 - 57.5 = 8.5

(b) Data without the eight day's measurement.

Raw data: [60,58,64,64,68,50,57]

Sorted data: [50,57,58,60,64,64,68]

Sample size = 7 (odd)

mean = 60.143

median = 60

1st quartile = 57

3rd quartile = 64

IQR = 64 -57 = 7

Answers:

1. The average is the same with or without the 8th day's data. FALSE

2. The median is the same with or without the 8th day's data. FALSE

3. The IQR decreases when the 8th day is included. FALSE

4. The IQR increases when the 8th day is included. TRUE

5. The median is higher when the 8th day is included. TRUE

6 0

3 years ago

The ratio of the length of an airplane wing to its width is 9 to 1. If the length of a wing is 40.4 meters, how wide must it b

VARVARA [1.3K]

The ratio of length to width is 9:11 is to 9 as x is to 40.41/9 = x/40.4 x = 40.4/9 = 4.48888.. meters

4 0

3 years ago

Select the equation of the line parallel to the equation y = -2x - 7 that passes through the point (3, 1). y = -2x + 7 y = -2x +

Vilka [71]

Y - y₁ = m(x - x₁)
y - 1 = -2(x - 3)
y - 1 = -2(x) + 2(3)
y - 1 = -2x + 6
+ 1 + 1
y = -2x + 7

The answer is A.

7 0

3 years ago

Choose the equation of a circle with radius 6 and center (2, -3).

Rufina [12.5K]

Answer: $(x-2)^2 + (y+3)^2 = 36\\\\$

Work Shown:

$(x-h)^2 + (y-k)^2 = r^2\\\\(x-2)^2 + (y-(-3))^2 = 6^2\\\\(x-2)^2 + (y+3)^2 = 36\\\\$

Note that (h,k) = (2,-3) is the center and r = 6 is the radius. The last line is not expanded out using the FOIL rule because its common practice to leave it in $(x-h)^2 + (y-k)^2 = r^2\\\\$ form. This form allows the reader to quickly determine the center and radius (rather than have to do a lot of algebraic steps before hand).