Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
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- Consider the following system of linear equations in the variables a,b,c,d:
5a-3b 7c - 2d = 2
2ab
2c+ 5d = -3
→ (*)
4a 3b 5d = 3
6a b+2c+ 7d = −7
(a) Solve the system (*) by using Gauss elimination method.
(b) Solve the system (*) by using Cramer's rule method.
Solve for a 25 55 30 a=?
9:41
…
93
Applying an Exponential Function to
Newton's Law of Cooling
60. Water in a water heater is originally
Aa ←
122°F. The water heater is shut off and
the water cools to the temperature of the
surrounding air, which is 60°F. The water
cools slowly because of the insulation
inside the heater, and the value of k is
measured as 0.00351.
a. Write a function that models the
temperature T (t) (in °F) of the water t
hours after the water heater is shut off.
b. What is the temperature of the water
12 hr after the heater is shut off? Round
to the nearest degree.
c. Dominic does not like to shower with
water less than 115°F. If Dominic waits
24 hr. will the water still be warm
enough for a shower?
Mixed Exercises
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- Please use the infinite series formula and specify how you did each step. Thank you.arrow_forward8) Solve the given system using the Gaussian Elimination process. 2x8y = 3 (-6x+24y = −6arrow_forward7) Solve the given system using the Gaussian Elimination process. (5x-4y = 34 (2x - 2y = 14arrow_forward
- 33 (a) (b) Let A(t) = = et 0 0 0 cos(t) sin(t) 0-sin(t) cos(t)) For any fixed tЄR, find det(A(t)). Show that the matrix A(t) is invertible for any tЄ R, and find the inverse (A(t))¹.arrow_forwardUse the infinite geometric sum to convert .258 (the 58 is recurring, so there is a bar over it) to a ratio of two integers. Please go over the full problem, specifying how you found r. Thank you.arrow_forwardH.w: Find the Eigen vectors for the largest Eigen value of the system X1+ +2x3=0 3x1-2x2+x3=0 4x1+ +3x3=0arrow_forward
- need help with 5 and 6 pleasearrow_forward1) Given matrix A below, answer the following questions: a) What is the order of the matrix? b) What is the element a13? c) What is the element a₁₁? 4 -1arrow_forward[25 points] Given the vector let v = ER² and the collection of vectors ε = E-{)·()}-{☹) (9)} = {(A)·(9)}· B: = and C = · {(6)·(})}· answer the following question. (a) (b) (c) (d) (e) verify Verify is a basis for R² and find the coordinate [] of under ε. Verify B is a basis for R2 and find the coordinate []B of ʊ Verify C is a basis for R2 and find the coordinate []c of under ε. under ε. Find the change-of-basis matrix [I]+B from basis B to basis ε, and EE+BUB Find the change-of-basis matrix [I]B+ε from basis Ɛ to basis B, and verify [U]B= [] B+EVEarrow_forward
- Explain the following terms | (a) linear span (b) dimension of vector space (c) linearly independent (d) linearly dependent (e) rank of matrix Aarrow_forward3. Let u = 3/5 √ = and = -4/5 -() Define V span{ū, }. (a) (b) (c) Show that {u, } is orthonormal and forms a basis for V. Explicitly compute Projy w. Explicitly give a non-zero vector in V+.arrow_forwardIs 1.1 0.65 -3.4 0.23 0.4 -0.44 a basis for R3? You must explain your answer 0arrow_forward
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