  # hs al2 l3 s2 06 unit test part 2

Topics: Multiplication, Ring, Addition / Pages: 2 (348 words) / Published: Dec 15th, 2014
Name:
Date:
Unit Test, Part 2: Vectors and Matrices
Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit.

(a) A =
A =
Hence this is the matrix A.

(b) a12 indicating 26 which is 2nd column element of 1st row. It represents the total medium size button sweaters available in the store.

(c) Elements in the second row are 64, 17 and 35.
Add them we will get 64+17+35 = 116. This number represents the total number of Zipper’s sweaters of different types and sizes available in the store.

(d) Large sweaters represent by the last column of both the matrices. Since A is the sum of those two matrices hence A’s last column is also representing the Large sweaters stock in the store.
So, total large sweaters in the store = 42 + 35 = 77.

(e) For that we need to subtract Boy’s matrix from Girl’s matrix, lets say the resultant matrix will be B then:
B =.
B =
First row is showing more girls than boys for button and second row is showing for zipper.

a. Let we will get matrix A after multiplication, then:
A =
A=.
Hence this 1 x 4 matrix A is the result of matrix multiplication.

b. In matrix A, 1st column is for Nov, 2nd column is for Dec, 3rd column is for Jan and 4th column is for Feb.
We need to compare Jan and Dec so we just need to subtract the 2nd column value from 3rd column value.
Hence 1388 – 1024= 364 is the answer of part b.

So, (-5, 8) is the answer for this question.

Matrix equation is: A X = B, where A, X and B are matrices and given by:
A =, X = and B =
We need to find X.
Hence we need to multiply both the sides by A-1.
We have A given.
|A| = 1(-5) – (-2)(3) = -5 – (-6) = -5 + 6 = 1.
Cofactor for A11 = (-1)1+1(-5) = -5
Cofactor for A12 = (-1)1+2(3) = -3
Cofactor for A21 = (-1)2+1(-2) = 2
Cofactor for A22 = (-1)2+2(1) = 1.
Therefore,

Hence,

So,
X = A-1B = Hence x = 8 and y = 3 is the