Question

can someone help me with 4 and 5?

Answer 1

what do you know about matrix multiplication?

Answer 2

that you add the first and last numbers

Answer 3

do you understand a dot product between 2 matrix?

Answer 4

no

Answer 5

ok then, we're multiplying a 2x2 matrix by a 2x2 matrix
we know that multiplication is possible because the middle are both 2
2x (2 = 2) x2

and the resulting matrix will be a 2x2 matrix
ex. (1x3)*(3x1) is possible and the resulting matrix will be a 1x1 matrix

for dot product, if we have 2 vectors (1x n) or (n x1)
the dot product is equal to the entries multiplied to their respective entry then added together
ex. \[\left(\begin{matrix}1 \\ 2 \\3 \end{matrix}\right) * \left(\begin{matrix}1 \\ 2\\3 \end{matrix}\right)\] the dot product of those 2 matrices
=1*1 +2*2+3*3=14

Answer 6

for matrix multiplication, if you're finding the entry (i,j) of a matrix
the entry(i,j) is equal to the dot product of row i of the first matrix and column j

ex.\\[A=\left[\begin{matrix}1 & 2 \\ 3 & 4\end{matrix}\right]\ B=\left[\begin{matrix}2 & 3 \\ 4 & 5\end{matrix}\right]\]
for A*B
the entry of (1,1) would be =1*2+2*4=10
entry of (1,2) =1*3+2*5=13
\[A*B=\left[\begin{matrix}10 & 13 \\ ? & ?\end{matrix}\right]\]
and so on and so forth

Answer 7

any questions?

Answer 8

would 4 be a?

Answer 9

5=c?

Answer 10

4 is not a, just look at the first entry
the dot product [1 6] and [1 -3] is not equal to 1

Answer 11

5 is incorrect as well, again just look at the entry (1,1)

Answer 12

4=b?

Answer 13

ok before you continue guessing,
what is the dot product of [1 6] and [1 -3] ?