Find the dimension of the subspace spanned by the given vectors. [Start 3 By 1 Matrix 1st Row 1st Column 1 2nd Row 1st Column ne
gative 2 3rd Row 1st Column 0 EndMatrix ]1 −2 0 , [Start 3 By 1 Matrix 1st Row 1st Column negative 1 2nd Row 1st Column 3 3rd Row 1st Column 1 EndMatrix ]−1 3 1 , [Start 3 By 1 Matrix 1st Row 1st Column 2 2nd Row 1st Column 1 3rd Row 1st Column 5 EndMatrix ]2 1 5 , [Start 3 By 1 Matrix 1st Row 1st Column negative 1 2nd Row 1st Column 1 3rd Row 1st Column 1 EndMatrix ]−1 1 1 The dimension of the subspace spanned by the given vectors is nothing
1 answer:
Answer:
4
Step-by-step explanation:
Given the following column vectors
(1, -2, 0), (-1, 3, 1), (2, 1, 5) and (-1, 1, 1)
Before we can get the dimension of the vector, the following steps must be followed;
Step 1:
We need to transform the vectors given into a matrix form and then reduce the resulting matrix.
Step 2:
Then we generated the basis of the matrix (new set of column vectors from the reduced matrix).
Step3:
The total number of column vectors generated will be equivalent to the dimension of the vectors.
The dimension spanned by the set of vectors is 4
Check the attachment for calculation
You might be interested in
Answer:
95%
Step-by-step explanation:
Upper limit = 8.09 cm
Lower limit = 6.41 cm
Distribution mean = 7.25 cm
Standard deviation = 0.42 cm
The number of standard deviations from the mean of the upper and lower limits are, respectively:
Both limits are two standard deviations away from the mean.
According to the empirical rule, in normal distributions, 95% of the data falls within two standard deviations of the mean. Therefore, 95% of the apples have diameters that are between 6.41cm and 8.09 cm.