Download Chapter 8 Vocabulary

Chapter 8 Vocabulary
Section 8.1 Vocabulary
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A _________ is a streamlined technique solving systems of ____________ equations.
A matrix having m rows and n columns is said to be of ____________ m x n.
A matrix that has only one row is called a ________ _________, and a matrix that has only one
column is called a ___________ _________.
4. For a square matrix, the entries a11, a22, a33 ... ann are the __________ _________ entries.
5. The vertical dots in an _______________ matrix separate the coefficients of the ____________
system from the ______________ terms.
6. A matrix derived from a system of linear equations (each written in standard form with the
constant term on the right) is the ____________ _____________ of the system.
7. The matrix derived from the ______________ of the system (but not including the constant terms)
is the _______________ _______________ of the system.
8. A matrix is __________ if the number of rows equals the number of columns.
9. Two matrices are called ____________ if one of the matrices can be obtained from the other by a
sequence of elementary row operations.
10. A matrix in row-echelon form is in ___________ ____________ ____________ if every column
that has a leading 1 has zeros in every position above and below its leading 1.
11. The process of using row operations to write a matrix in reduced row-echelon form is called
_____________ ________________.
12. Gauss Jordan eliminations is named after ___________________________ and
_____________________ and continues the reduction process until a ______________
_________________ is obtained.
Section 8.2 Vocabulary
1.
Matrices can be used to solve real life problems such as
______________________________________.
2. Two matrices are ___________ if all of their corresponding entries are equal.
3. When performing matrix operations, real numbers are often referred to as ___________.
4. A matrix can be denoted by an ______________ ______________ such as A, B, or C.
5. A matrix can be denoted by a _______________________ of numbers.
6. A matrix consisting entirely of zeros is called a __________ matrix and is denoted by
___________.
7. The n x n matrix consisting of 1’s on its main diagonal and 0’s elsewhere is called the
____________ matrix of order n.
8. ______________ __________a British mathematician invented matrices around _____________.
________________ and __________________ and ___________________ are credited with
developing “matrix algebra.”
In exercises 9 and 10, match the matrix property with the correct form. A, B, and C are matrices of order m
x n, and c and d are scalars.
9.
(a) (c + d)A = cA + dA
(b) A + (B + C) = (A + B) + C
(c) A + B = B + A
(d) (cd)A = c(dA)
(e) 1A = A
(i) Distributive Property
(ii) Commutative Property of Matrix Addition
(iii) Scalar Identity Property
(iv) Associative Property of Matrix Addition
(v) Associative Property of Scalar Multiplication
(a) A(B + C) = AB + AC
(b) A + 0 = A
(c) A(BC) = (AB)C
(d) c(AB) = A(cB)
(i) Distributive Property
(ii) Additive Identity of Matrix Addition
(iii) Associative Property of Multiplication
(iv) Associative Property of Scalar Multiplication
10.
Section 8.3 Vocabulary
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In a __________ matrix, the number of rows equals the number of columns.
In there exists an n x n matrix A-1 such that AA-1 = In = A-1A, then A-1 is the ___________ of A.
Most graphing utilities can find the invers of a square matrix. To do so you may have to use the
__________ key _________.
If a matrix A has an inverse, it is called invertible or ____________; if it does not have an inverse,
it is called ____________.
If A is an invertible matrix, the system of linear equations represented by AX = B has a unique
solution given by X = ____________.
Section 8.4 Vocabulary
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Both det(A) and │A│ represent the ___________ of the matrix A.
__________________ are often used in other branches of mathematics. For example they are used
when changes in variables are made in _____________.
The ____________ Mij of the entry aij is the determinant of the matrix obtained by deleting the ith
row and jth column of the square matrix A.
The ____________ Cij of the entry aij of the square matrix A is given by (-1)i + j Mij.
The method of finding the determinant of a matrix of order 2 x 2 or greater is called __________
by ____________.
Section 8.5 Vocabulary
1.
The method of using determinants to solve a system of linear equations is called __________
__________.
2. Three points are __________ if the points lie on the same line.
3. The area A of a triangle with vertices (x1, y1), (x2,y2), and (x3, y3) is given by _______________.
4. You can check the _________ of a triangle by plotting points on the ___________________ and
use the formula A = 1/2bh.
5. Cramer’s rule can be used to solve real life problems. Such as finding a ____________ model for
the number of ____________________________________________.
6. A message written according to a secret code is called a _____________.
7. Cramer’s rule was named after _________________________. This rule uses determinants to
write the solution of a system of ________________ equations
8. To encode a message, choose an invertible matrix A and multiply ____________ row matrixes by
A (on the right) to obtain ______________ row matrices.
9. During World War II, ___________ soldiers created code using their native language to send
messages between battalions. Native words were assigned to represent ____________ in the
__________ alphabet, and they created a number of expressions for important ______________
terms.
10. Use a computer to research information another type of Cryptography. Write a short paragraph
describing how mathematics is used to code and decode messages. Yes I am serious! And you all
better have different answers!
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