Question

matrix question:
if\[A=\left[\begin{matrix}-5&-2&-4\\0&-4&4\end{matrix}\right]\]and\[C=\left[\begin{matrix}7&-5\\-4&10\end{matrix}\right]\]then what is\[-5AA^{T}+4C\]

Answer 1

http://openstudy.com/study?signup#/updates/4fa5cc07e4b029e9dc35b2c0

Answer 2

ah much better :)

Answer 3

definitely better

Answer 4

is A even invertible?I don't think so.

Answer 5

oh you want transpose...

Answer 6

how do i do this?

Answer 7

you are not familiar with the transpose part?
all you do to find \(A^T\) is change the \(i\) an \(j\) locations of each element switch
for instance....

Answer 8

http://tutorial.math.lamar.edu/Classes/LinAlg/MatrixArithmetic.aspx
example 10 shows how to do transposes

Answer 9

OK

Answer 10

example:\[\text{ if }A=\left[\begin{matrix}a&b\\c&d\\e&f\end{matrix}\right]\text{ then }A^T=\left[\begin{matrix}a&c&e\\b&d&f\end{matrix}\right]\]

Answer 11

it sort of "flips" the matrix

Answer 12

OK AND THEN ITS FLIPPED, HOW WOULD I FIND THE ANS?

Answer 13

DO I HAVE TO TRANSPOSE C TOO?

Answer 14

could you please not use all caps, it makes it seem as though you are shouting


you matrix A by it's transpose
do you not know how to multiply the two matrices?

Answer 15

you matrix multiply A by...*

Answer 16

Ok no caps...sorry

Answer 17

multiplu matrix a when transposed by -5

Answer 18

is that correct?

Answer 19

no, -5 is a scalar
there is no such thing as transposing "by" some number
there is only just the transpose

Answer 20

ok so i just multiply a by -5?

Answer 21

right
first take the transpose
then multiply \(AA^T\)
then multiply by 5
then subtract 3C

Answer 22

ok lets see

Answer 23

its + 4c / not subtract 3 c

Answer 24

well I'm glad someone's paying attention ;)

Answer 25

-5*a*a^t = (-125, -50,-100)
(-50,-100,40)
(-100,40,160)

Answer 26

you should get a 2x2 matrix from the multiplication

Answer 27

how do i add 4 c...the dimensions dont match

Answer 28

ok when u say " then multiply A*AT" - i will have to multiply the transposed by A - which is a 2 x 3 * a 3 x 3 - which gives a 3 x 3

Answer 29

\[A_{i\times j}\implies A_{j\times i}^T\]where \(i\) is the number of rows and \(j\) is the number of columns, so\[A_{i\times j}A_{j\times i}^T=B_{i\times i}\]

Answer 30

that means you final matrix will be square, having the the same number of columns as it had rows
in this case its\[A_{2\times3}A_{3\times2}^T=B_{2\times2}\]so the dimensions are \(2\times2\)

Answer 31

ok

Answer 32

i see