Biocalculus
15th Edition
ISBN: 9781133109631
Author: Stewart, JAMES, Day, Troy
Publisher: Cengage Learning,
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(b) A= np.array([[1,2],[3,4],[10,6]])
(c) A= np.array([[1,2,3],[3,4,5],[4,10,6]])
What is the vector for b, and c?
Consider the following matrix and vector:
1 0 1
---A
A = -2 1 -4 and x 1₂
0-3 6
Given that Ax-0 and x₂-1, find x₂-
01
(Section 5.3)
3. a. i. Show that the vectors v₁ = (1, 2, 3, 4), №₂ = (0, 1, 0, −1), and
√3 = (1,3,3,3) form a linearly dependent set in IR".
b.
ii. Express each vector in part i. as a linear combination of the other two.
Prove that if {v₁, 02, 03} is a linearly independent set of vectors, then so
are {vi, v3), and {₂}.
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- Matrix C represents the number of calories burned per hour of exercise riding a bicycle, running, and walking for individuals of two different weights. Matrix N represents the number of hours spent working out with each type of activity for a given week. Find the product CN and interpret its meaning. Bike Run Walk 320]120-lb person 480 ]180-lb person 400 500 550 780 6 Bike N = | 3 Run 5]Walkarrow_forwardConsider the Matrixarrow_forwardA firm orders 12, 30 and 25 items of goods G1, G2 and G3. The cost of each item of G1, G2 and G3 is 8, 30 and 15 euros, respectively. Write down suitable price and quantity vectors and use matrix multiplication to work out the total cost of the order. Write down the new price vector when the cost of G1 rises by 20%, the cost of G2 falls by 10% and the cost of G3 is unaltered. Use matrix multiplication to work out the new cost of the order and hence find the overall percentage change is total cost.arrow_forward
- The columns of A are n vectors from Rm. If they are linearly independent, what is the rank of A? If they span Rm, what is the rank? If they are a basis for Rm, what then? Looking ahead: The rank r counts the number of __ columns.arrow_forwardCompute the third row of the product (if it exists) by summing an appropriate linear combination of row vectors. -3 -1 - 1 3 -3 -2 -3 -3 2 3 4 5 1 6 -1arrow_forward
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