Answer:
Check the ecplanation
Step-by-step explanation:
A set of three vectors in 
represents a matrix of 3 column vectors, and each vector containing 4 entries (that is, a matrix of 4 rows, and 3 columns).
Let A be that 4x 3 matrix. The columns of A span 
. if and only if A has a pivot position in each row. So, there are at most 3 pivot positions in the matrix A, but the number of rows is 4, therefore, there exist at least one row not having a pivot position. If A does not have a pivot position in at least one row, then the columns of A do not span . It implies that the set of 3 vectors of A does not span all of .
In general, the set of n vectors in represents a matrix of in rows, and n columns (an in x matrix). So, there are at most n pivot positions in the matrix A, but n is less than the number of rows. In therefore, there exist at least one row that does not contain a pivot position.
And, hence the set of n vectors of A does not span all of . for n < m
Answer:
10. 16 cubic cm
11. 5 and 1/3 cubic cm
Step-by-step explanation:
4 · 4 · 2 = 32
32 times 1/2 = 16
2 · 2 · 4 = 16
16 times 1/3
The least common multiple of 96, 144, and 224 is 2016.
Hope this helps! :D
Answer:
$82 sundaes
$74 banana split
Step-by-step explanation:
Step one :
Given data
Cost of sundaes =$2 each
Cost of banana split =$3 each
Let the number of sundaes bought be x
And the number of banana split bought be y
The total is x+y
The shop sold 8 more Sundaes than the Banana split
x=8+y—-------1
Total amount made = $156
Therefore the system of equation for the situation is
x=8+y----—----------1
2x+3y=156---------2
But x=8+y
8+y+y=156
8+2y=156
2y=156-8
2y=148
Divide both sides by 2
y=148/2
y=74
On That day they sold $74 banana split
And also they sold x=8+74=$82 sundaes
y=4x-3(4,1)x2 (2-0) perpedkdkke
