row- horizontal elements column- vertical elements 3 x 2 matrix
TRANSCRIPT
Row- horizontal elementsColumn- vertical elements
3 x 2 matrix
310
221A
412
403B
2BA
If A and B are both m × n matrices then the sum of A and B, denoted A + B, is a matrix obtained by adding corresponding elements of A and B.
add these
310
221A
412
403B
22BA
add these
310
221A
412
403B
622BA
add these
310
221A
412
403B
2
622BA
add these
310
221A
412
403B
02
622BA
add these
310
221A
412
403B
102
622BA
add these
If A and B are both m × n matrices then the difference of A and B, denoted A - B, is a matrix obtained by subtracting corresponding elements of A and B.
ABBA
CBACBA )()(
The multiplication of matrices is easier shown than put into words. You multiply the rows of the first matrix with the columns of the second adding products
140
123A
13
31
42
B
Find AB
First we multiply across the first row and down the first column adding products. We put the answer in the first row, first column of the answer.
23 1223 5311223
140
123A
13
31
42
B
Find AB
We multiplied across first row and down first column so we put the answer in the first row, first column.
5AB
Now we multiply across the first row and down the second column and we’ll put the answer in the first row, second column.
43 3243 7113243
75AB
Now we multiply across the second row and down the first column and we’ll put the answer in the second row, first column.
20 1420 1311420
1
75AB
Now we multiply across the second row and down the second column and we’ll put the answer in the second row, second column.
40 3440 11113440
111
75AB
Notice the sizes of A and B and the size of the product AB.
To multiply matrices A and B look at their dimensions
pnnm MUST BE SAME
SIZE OF PRODUCT
If the number of columns of A does not equal the number of rows of B then the
product AB is undefined.
6
BA
126
BA
2126
BA
3
2126
BA
143
2126
BA
4143
2126
BA
9
4143
2126
BA
109
4143
2126
BA
4109
4143
2126
BA
Now let’s look at the product BA.
13
31
42
B
140
123A
BAAB
23
32
can multiply
size of answer
across first row as we go down first column:
60432
across first row as we go down second column:
124422
across first row as we go down third column:
21412
across second row as we go down first column:
30331
across second row as we go down second column:
144321
across second row as we go down third column:
41311
across third row as we go down first column:
90133
across third row as we go down second column:
104123
across third row as we go down third column:
41113
Completely different than AB!
Commuter's Beware!
13
Ca
K
H He
Li
B
Be
C N O FNe
NaMg
Al Si P S Cl
Ar
0
50
100
150
200
250
0 2 4 6 8 10 12 14 16 18 20
Element
Ato
mic
Rad
ius
(pm
)
Atomic Radii refers to the size of the atom
It is measured from the nucleus to the edge of the atom
What is the trend?The radius
increases as you go down a group.
The radius decreases as you
go across a period
18
period 1
period 2
period 3
1p+
3p+ 4n0
11p+ 12n0
As we move down a group, the valence electron(s) move farther away from the nucleus because the period number tells us what energy level the valence electron is on
Group 1
Li
+++
Be
++++
B
+++++
Period 2
Going ACROSS a period proton # increases . More protons means greater attraction between nucleus and valence electron(s).
The greater attraction also means that valence electrons are brought closer to the nucleus, thus smaller atomic radius results.
Group 1 Group 2 Group 13
Barium or Magnesium? Barium
Sodium
Cesium
• Lithium or Sodium?
• Potassium, Argon, Neon, or Cesium?
21
Ionization energy is the energy required to remove an electron from an atom.
What is the trend?Why?
Decreases down a group
SHIELDING Interior electrons
prevent the nucleus from pulling on valence electrons
1p+
3p+ 4n0
11p+ 12n0
Increases across a period, or row Increased electrostatic attraction
24
Li
+++
Be
++++
B
+++++
Peroid 2
Group 1 Group 2 Group 13
25
Electronegativity is a measure of the ability of an atom in a chemical compound to attract electrons
What is the trend?Why?
Decreases down a group
SHIELDING Interior electrons
prevent the nucleus from pulling on valence electrons
1p+
3p+ 4n0
11p+ 12n0
Increases across a period Increased electrostatic attraction
28
Li
+++
Be
++++
B
+++++
Peroid 2
Group 1 Group 2 Group 13
Atomic Radius: down and left Ionization Energy: up and rightElectronegativity: up and right
WHY? Answer is always shielding down a group
and increased electrostatic attraction across a period
29
Matrices Worksheet (page 4 of the packet)
Encode a 10-character message using the matrix given (due Wed)