Download Matrix multiplication 3x4 matrix 4x2 matrix The multiplication is legal

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

page
1
page
2
Document related concepts
no text concepts found
Transcript 
Matrix multiplication
3x4 matrix
4x2 matrix
The multiplication is legal since
1
number of columns of A is the
2345
A= 5432
3
B = 3 –2
1212
4
same as the number of rows of B.
1
The dimension of the result equals
3 5
the number of rows of A times the
number of columns of B.
3x2 matrix
AXB =
2X1+3X3+4X4+5X3 2X3+3(-2)+4X1+5X5
= 42 29
5X1+4X3+3X4+2X3 5X3+4X(-2)+3X1+2X5
= 35 20
1X1+2X3+1X4+2X3 1X3+2X(-2)+1X1+2X5
= 17 10
Vector multiplication
A = Axi + Ayj + Azk
B = Bxi + Byj + Bzk
A · B = AxBx + AyBy + AzBz
dot product
A X B = i (AyBz – AzBy) + j (AzBx – AxBz) + k (AxBy – AyBx)
cross product
Examples
A = i + 2j + 3k
B = 5 i – 3j + 4k
A · B = 1X5 + 2X(-3) + 3X4 = 11
a scalar
A X B = i (8 – (-9)) – j (15-4) + k ((–3) – 10) = 17 i + 11j – 13k
a vector
Determinants of matrices (always scalars)
2x2
2 5
3 4
= 2X4 – 3X5 = –7
3x3
2 4 1
–1 5 3
=
2(5X1–2X3) –4((–1)X1–3X3) +1((–1)X2–3X5) = 21
3 2 1
Higher dimensions require a knowledge of cofactors, which you will get in your
linear algebra course.
Related documents