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quester [9]
3 years ago
8

Box all final answers. Little to no work will reccive little to no credit! I. (5 points) Let A and B be 4 x 4 matrices, with det

(A) =-3 and det(B) = 2: Compute (a) det(AB) (b) det(B5) (c) det(2A) (d) det(ATA) (e) det(B-AB)
Mathematics
1 answer:
FinnZ [79.3K]3 years ago
6 0

Answer: a) -6, b) 32, c) -48, d) 9, e) -12

Step-by-step explanation:

Since we have given that

A and B are 4 × 4 matrices.

Here,

det (A) = -3

det (B) = 2

We need to find the respective parts:

a) det (AB)

\mid AB\mid=\mid A\mid.\mid B\mid\\\\\mid AB\mid=-3\times 2=-6

b) det (B⁵ )

\mid B^5\mid=\mid B\mid ^5=2^5=32

c) det (2A)

Since we know that

\mid kA\mid =k^n\mid A\mid

so, it becomes,

\mid 2A\mid =2^4\mid A\mid=16\times -3=-48

d) \bold{det(A^TA)}

Since we know that

\mid A^T\mid=\mid A\mid

so, it becomes,

\mid A^TA\mid=\mid A^T\mid \times \mid A\mid=-3\times -3=9

e) det (B⁻¹AB)

As we know that

\mid B^{-1}\mid =\mid B\mid

so, it becomes,

\mid B^{-1}AB}\mid =\mid B^{-1}.\mid \mid A\mid.\mid B\mid=2\times -3\times 2=-12

Hence, a) -6, b) 32, c) -48, d) 9, e) -12

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Gala2k [10]

The percentage of students age 15 and above travel to school by bus is 47%

<h3>How to complete the table?</h3>

The table of values is given as:

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15                            18                 165

Age 15 and above    65                                 195

Column totals          152          110        98      360

Using the column total of column 1, we have:

Under age 15 + 65 = 152

This gives

Under age 15 = 87

Using the column total of column 2, we have:

Age 15 and above + 18 = 110

This gives

Age 15 and above  = 92

Using the row total of row 1, we have:

Car + 87 + 18 = 165

This gives

Car = 60

Using the row total of row 2, we have:

Car + 65 + 92 = 195

This gives

Car = 38

So, the complete frequency table is

                     Method of Travel to School

                            Walk/Bike    Bus    Car Row totals

Under age 15           87              18      60        165

Age 15 and above    65          92        38        195

Column totals          152          110        98      360

The percentage of students age 15 and above travel to school by bus is:

Percentage = 92/195 * 100%

This gives

Percentage = 47%

Read more about frequency table at:

brainly.com/question/12576014

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Answer:

Step-by-step explanation:

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