 7.6.7.6.1: Fill in the blanks. In a _______ matrix, the number of rows equals ...
 7.6.7.6.2: Fill in the blanks. If there exists an matrix such that then is cal...
 7.6.7.6.3: If there exists an matrix such that then is called the _______
 7.6.7.6.4: In Exercises 16, show that is the inverse of A.
 7.6.7.6.5: In Exercises 16, show that is the inverse of A.
 7.6.7.6.6: In Exercises 16, show that is the inverse of A.
 7.6.7.6.7: In Exercises 710, use the matrix capabilities of a graphing utility...
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 7.6.7.6.11: In Exercises 1120, find the inverse of the matrix (if it exists).
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 7.6.7.6.20: In Exercises 1120, find the inverse of the matrix (if it exists).
 7.6.7.6.21: In Exercises 2128, use the matrix capabilities of a graphing utilit...
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 7.6.7.6.28: In Exercises 2128, use the matrix capabilities of a graphing utilit...
 7.6.7.6.29: In Exercises 29 36, use the formula on page 545 to find the inverse...
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 7.6.7.6.36: In Exercises 29 36, use the formula on page 545 to find the inverse...
 7.6.7.6.37: In Exercises 3740, find the value of the constant such that B A1.
 7.6.7.6.38: In Exercises 3740, find the value of the constant such that B A1.
 7.6.7.6.39: In Exercises 3740, find the value of the constant such that B A1.
 7.6.7.6.40: In Exercises 3740, find the value of the constant such that B A1.
 7.6.7.6.41: In Exercises 41 44, use the inverse matrix found in Exercise 13 to ...
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 7.6.7.6.44: In Exercises 41 44, use the inverse matrix found in Exercise 13 to ...
 7.6.7.6.45: In Exercises 45 and 46, use the inverse matrix found in Exercise 17...
 7.6.7.6.46: In Exercises 45 and 46, use the inverse matrix found in Exercise 17...
 7.6.7.6.47: In Exercises 47 and 48, use the inverse matrix found in Exercise 28...
 7.6.7.6.48: In Exercises 47 and 48, use the inverse matrix found in Exercise 28...
 7.6.7.6.49: In Exercises 4956, use an inverse matrix to solve (if possible) the...
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 7.6.7.6.61: Computer Graphics In Exercises 6164, the matrix product performs th...
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 7.6.7.6.65: Investment Portfolio In Exercises 6568, consider a person who inves...
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 7.6.7.6.69: Circuit Analysis In Exercises 69 and 70, consider the circuit in th...
 7.6.7.6.70: Circuit Analysis In Exercises 69 and 70, consider the circuit in th...
 7.6.7.6.71: In Exercises 7174, a small home business specializes in gourmetbak...
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 7.6.7.6.75: Coffee A coffee manufacturer sells a 10pound package of coffee for...
 7.6.7.6.76: Flowers A florist is creating 10 centerpieces for the tables at a w...
Solutions for Chapter 7.6: The Inverse of a Square Matrix
Full solutions for Precalculus With Limits A Graphing Approach  5th Edition
ISBN: 9780618851522
Solutions for Chapter 7.6: The Inverse of a Square Matrix
Get Full SolutionsThis textbook survival guide was created for the textbook: Precalculus With Limits A Graphing Approach, edition: 5. Chapter 7.6: The Inverse of a Square Matrix includes 76 full stepbystep solutions. Since 76 problems in chapter 7.6: The Inverse of a Square Matrix have been answered, more than 33152 students have viewed full stepbystep solutions from this chapter. Precalculus With Limits A Graphing Approach was written by and is associated to the ISBN: 9780618851522. This expansive textbook survival guide covers the following chapters and their solutions.

Big formula for n by n determinants.
Det(A) is a sum of n! terms. For each term: Multiply one entry from each row and column of A: rows in order 1, ... , nand column order given by a permutation P. Each of the n! P 's has a + or  sign.

Change of basis matrix M.
The old basis vectors v j are combinations L mij Wi of the new basis vectors. The coordinates of CI VI + ... + cnvn = dl wI + ... + dn Wn are related by d = M c. (For n = 2 set VI = mll WI +m21 W2, V2 = m12WI +m22w2.)

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Cyclic shift
S. Permutation with S21 = 1, S32 = 1, ... , finally SIn = 1. Its eigenvalues are the nth roots e2lrik/n of 1; eigenvectors are columns of the Fourier matrix F.

Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.
Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

Eigenvalue A and eigenvector x.
Ax = AX with x#O so det(A  AI) = o.

Elimination matrix = Elementary matrix Eij.
The identity matrix with an extra eij in the i, j entry (i # j). Then Eij A subtracts eij times row j of A from row i.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

GramSchmidt orthogonalization A = QR.
Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

Hankel matrix H.
Constant along each antidiagonal; hij depends on i + j.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Network.
A directed graph that has constants Cl, ... , Cm associated with the edges.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Permutation matrix P.
There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or 1) based on the number of row exchanges to reach I.

Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.
Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

Reduced row echelon form R = rref(A).
Pivots = 1; zeros above and below pivots; the r nonzero rows of R give a basis for the row space of A.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Vandermonde matrix V.
V c = b gives coefficients of p(x) = Co + ... + Cn_IXn 1 with P(Xi) = bi. Vij = (Xi)jI and det V = product of (Xk  Xi) for k > i.