For Exercises 27-32, perform the elementary row operations on [ 1 5 6 2 2 1 5 1 4 − 2 − 3 10 ] . (See Example 2) R 1 ⇔ R 2
For Exercises 27-32, perform the elementary row operations on [ 1 5 6 2 2 1 5 1 4 − 2 − 3 10 ] . (See Example 2) R 1 ⇔ R 2
Solution Summary: The author explains that the matrix obtained on elementary row operation R_1iff — if row interchange is applied on above matrix, the elements of first and second rows are interchanged.
without doing any row operations, explain in a short sentence why
137
0506
0028
000 10
[1 2 31
A= 1 2 3 is not invertible and why B
1
2
3
is invertible
EXERCISE 8
1.
DON'T SIMPLIFY the following. ONLY INDICATE whether or not the
result of the product will be a sum or difference of two cubes.
(2x+1)(x-2x+1)
(x-3)(x+3x+9)
(3x +2y)(x -6xy+4y)
(4a- 3b)(16a +12ab +9b)
+ 60a+9)
(10a-3)(100a
-
(a)
(x+3)(x' -3x+9)
(x-3)(x - 3x+9)
(3x+2y)(x -6xy+4y')
(b)
(c)
(d)
(e)
(f)
(g)
(h)
Factorise the following
x'-1
2.
(a)
(b)
x+1
(c)
64x-y
a'b!
8
(d)
125 – 729x
(e)
(f)
5x +40
x' +216
27
- 216
(g)
8a-64a
(h)
-x'-27 (i)
8-(a-1)
(k) +
G)
(1)
Consider x-64
(a)
3.
Factorise the above expression by using the difference of two
cubes method first.
Factorise the above expression by using the difference of two
squares method first.
The one seems to factorise further than the other. Why is this so?
(b)
(c)
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