18. Matrices

Question 1

Size of a matrix

Answer 1

r by c

• r* = number of rows
• c* = number of columns

Question 2

Name of entry in ith row and jth column

Answer 2

x_{i j}

Question 3

If r = 1, the matrix is called…

If c = 1, the matrix is called…

If r = c, the matrix is called…

Answer 3

a row matrix

a column matrix

a square matrix

Question 4

Scalar Multiplication

Answer 4

Each number in a matrix is multiplied by a constant.

Question 5

Addition and Subtraction

Answer 5

If two matrices are the same size, they can be added or subtracted by adding or subtacting corresponding entries.

Question 6

Conditions under which matrix multiplication is possible, where:

• A* is r₁ by c₁
• B* is r₂ by c₂

Answer 6

If c₁ = r₂, then AB is defined and has size r₁ by c₂.

Question 7

The entry x_{i j} of AB is…

Answer 7

the ith row of A times the jth column of B​.

Question 8

The determinant of a 2 by 2 matrix

Answer 8

Question 9

Finding determinants of n by n with TI-89

Answer 9

Question 10

Singular Matrix…

Nonsingular Matrix…

Answer 10

determinant = zero

determinant ≠ zero

Question 11

Identity Matrix

Answer 11

I • A = A

Question 12

Multiplicative inverse of a nonsingular matrix

Answer 12

A^–1A = AA^–1 = I

Question 13

Solving systems of equations using matrices on TI-89

x – y + 2z = –3

2x + y – z = 0

–x + 2y –3z = 7

⇒ x = –2, y = 7, z = 3

Answer 13