Question

Please help me with this question or tell me how to solve it I rlly need help :(

What is D⋅n⃗ ?

Answer 1

Your teacher made a mistake. The order of multiplication matters. AB is not the same as BA in matrix multiplication.

Matrix D is 2 x 2 while matrix n is 1 x 2. A vector is a special case of a matrix.

Notice how the inner dimensions marked in bold do not match up

• D = 2 x 2 and n = 1 x 2

This would mean the matrix product
`D \ \cdot \ \stackrel{\to}{n}` is not possible.

I have a feeling your teacher meant to say
`\stackrel{\to}{n} \ \cdot \ D` instead of
`D \ \cdot \ \stackrel{\to}{n}`

Swap the two sets of matrix dimensions to notice the inner values in bold matching up

• n = 1 x 2 and D = 2 x 2

This match tells us that
`\stackrel{\to}{n} \ \cdot \ D` is possible.

We'll apply the dot product of n with the first column of D to get:

-2*(-3) + (-1)*4 = 2

This result goes in the first box.

Apply the dot product of n with the second column of D to get:

-2*0 + (-1)*1 = -1

This is the result of the second box.

Therefore,

`\stackrel{\to}{n} \ \cdot \ D = \big < 2, -1\big >`