Introduction to Linear Algebra for Science and Engineering 2nd. Edition by Daniel Norman, Dan Wolczuk | 9780321748966 | 0321748964

Introduction to Linear Algebra for Science and Engineering

211 SOLVED PROBLEMS

Question: 4.3.3

Is the set B = { [ 1 2 -1 1 ] , [ 0 1 3 1 ] , [ 2 5 1 3 ]} a basis for the subspace Span B of M(2, 2)? ...

Verified Answer:

Since

\mathcal{B}

is a spanning set...

Question: 3.4.14

Consider the homogeneous system Ax = 0, where the coefficient matrix A = [ 1 2 0 3 4 0 0 1 5 6 ] is already in reduced row echelon form. By finding a basis for Null(A), determine the nullity of A and relate it to rank(A). ...

Verified Answer:

The general solution is

\vec{x}=t_{1}\left[...

Question: 7.3.1

Suppose that the experimenter’s data are as follows : t 1.0 2.1 3.1 4.0 4.9 6.0 y 6.1 12.6 21.1 30.2 40.9 55.5 ...

Verified Answer:

As in the earlier discussion, the experimenter wan...

Question: 7.2.2

Let W = Span {[ 1 0 0 1 ] . [ 1 0 1 0 ]}. Find W^⊥ in R^4. ...

Verified Answer:

We want to find all

\vec{v} = \begin{bmatri...

Question: 7.2.4

Use the Gram-Schmidt Procedure to find an orthonormal basis for the subspace of R^5 defined by S = Span {[ 1 1 0 1 1 ] , [ -1 2 1 0 1 ] , [ 0 1 1 1 2 ]}. ...

Verified Answer:

Call the vectors in the basis

\vec{w}_{1}, ...

Question: 9.1.1

Perform the following operations (a) (2 + 3i) + (S – 4i) ...

Verified Answer:

(2 + 3i) + (5 - 4i) = 2 + 5 + (3 - 4)i = 7 - i (b)...

Question: 9.1.8

Calculate the following using the polar form. (a) (2 + 2i)³ ...

Verified Answer:

(2 + 2i)³ = (2

\sqrt{2}e^{iπ/4})³ = (2 \sqr...

Question: 4.3.4

Is the set C = {3 + 2x + 2x², 1 + x², 1 + x + x²} a basis for P2? ...

Verified Answer:

Consider the equation

ao + a_{1}x + a_{2}x²...

Question: 7.1.4

Find the coordinates of x = [ 1 2 3 4 ] with respect to the orthonormal basis B = { 1/2 [ 1 1 1 1 ], 1/2 [ 1 -1 1 -1 ], 1/√2 [ -1 0 1 0 ], 1/√2 [0 1 0 -1 ]} ...

Verified Answer:

By Theorem 2, the coordinates

b_{1}, b_{2},...

Question: 7.1.9

Find the standard matrix of the linear transformation L : R³ → R³ that rotates vectors about the axis defined by the vector v= [ 1 1 1 ] counterclockwise through an angle π/3. ...

Verified Answer:

If the rotation were about the standard

x_{...