Row- horizontal elements Column- vertical elements 3 x 2 matrix
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
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.
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 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.
Find AB We multiplied across first row and down first column so we put the answer in the first row, first column. Now we multiply across the first row and down the second column and we’ll put the answer in the first row, second column. Now we multiply across the second row and down the first column and we’ll put the answer in the second row, first column. Now we multiply across the second row and down the second column and we’ll put the answer in the second row, second column. Notice the sizes of A and B and the size of the product AB.
To multiply matrices A and B look at their dimensions 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.
Now let’s look at the product BA. 2323 3232 can multiply size of answer across first row as we go down first column: across first row as we go down second column: across first row as we go down third column: across second row as we go down first column: across second row as we go down second column: across second row as we go down third column: across third row as we go down first column: across third row as we go down second column: across third row as we go down third column: Completely different than AB! Commuter's Beware!
__ = 0 A = 1 B = 2 C = 3 D = 4 E = 5 F = 6 G = 7 H = 8 I = 9 J = 10 K = 11 L = 12 M = 13 N = 14 O = 15 P = 16 Q = 17 R = 18 S = 19 T = 20 U = 21 V = 22 W = 23 X = 24 Y = 25 Z = 26
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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+ 4n 0 11p+ 12n 0 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 1Group 2Group 13
Barium or Magnesium? Barium Sodium Cesium Lithium or Sodium? Potassium, Argon, Neon, or Cesium?
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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+ 4n 0 11p+ 12n 0
Increases across a period, or row Increased electrostatic attraction 24 Li Be B Peroid 2 Group 1Group 2Group 13
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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+ 4n 0 11p+ 12n 0
Increases across a period Increased electrostatic attraction 28 Li Be B Peroid 2 Group 1Group 2Group 13
Atomic Radius: down and left Ionization Energy: up and right Electronegativity: 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)