# Matrix Multiplication Problems

- Posted by Brian Stocker
- Date June 17, 2020
- Comments 0 comment

### Operations with Matrices

Matrices are rectangular arrays, arranged in rows and columns. The dimension of an array is the number or rows times the number of columns.

Here, the dimension of the matrix below is 2 × 2

Two matrices with the same number of rows and columns can be added or subtracted element by element .

To multiply 2 matrices, the first matrix must have the same number of rows and the columns in the second.

**Finding the Determinate of a Matrix **

The determinant of a matrix is found by the formula:

det A = a_{11} detA_{11} – a_{12} detA_{12} + a_{13} detA_{13} – … + (- 1)1+n a_{1n}

detA_{1n}

n

= Σ(- 1)^{1+j} a_{1j} detA_{1j}

j=1

Here, A_{1j} named matrices are the submatrices obtained by

closing 1st row and column j in the matrix A. The closed row

and column elements are eliminated and the remaining entries

form A_{1j} submatrices. The determinant of a 2 x 2 matrix

is obtained by:

if A =

DET A = ab – cd.

### Multiplying Matrix

Find the determinant of matrix A

a. – 30

b. – 25

c. 10

d. 15

### Answer Key

**1.**

– (-1)

**2. D**

Notice that the dimensions for matrix A and B are 2 x 2

and 2 x 2, respectively. In matrix multiplication; the dimensions

are important. Since A * X = B, the dimensions

of matrix X should be 2 x 2. Let us say that matrix X is as

follows:

Now, let us write equations obtained from matrix multiplication:

1a + 4c = 2 … (I)

1b + 4d = 2 … (II)

1a + 3c = 5 … (III)

1b + 3d = 1 … (IV)

Now, we have 4 unknowns and 4 equations which means that we will be able to find the values of a, b, c and d. Using

equations (I) and (III), we will find a and c; using equations

(II) and (IV), we will find b and d:

1a + 4c = 2 … (I)

– / 1a + 3c = 5 … (III)

4c – 3c = 2 – 5

c = – 3

Inserting this value into equation (I): 1a + 4(- 3) = 2

a – 12 = 2

a = 14

1b + 4d = 2 … (II)

– / 1b + 3d = 1 … (IV)

4d – 3d = 2 – 1

d = 1

Inserting this value into equation (II): 1b + 4(1) = 2

b + 4 = 2

b = – 2

**Written by**, Brian Stocker MA., Complete Test Preparation Inc.

**Date Published:**Wednesday, June 17th, 2020

**Date Modified:**Thursday, December 29th, 2022

Got a Question? Email me anytime - Brian@test-preparation.ca

### You may also like

##### Hard Algebra Questions

Advanced Algebra Practice 1. Simplify expressions with radicals and rational exponents using properties of exponents A = 22a – 2 and B = 53 – 2a are given. Find the value of 404a – 2 in terms of A and …

##### Comprensión Lectora de Opción Múltiple

Aumenta tu Puntuación Passage 1 – El uso de las redes sociales en la adolescencia se relaciona con la pobreza Sueño, ansiedad. Fuente: [Por Agata Blaszczak-Boxe, publicado originalmente en Live Science, septiembre de 2015]. Según un nuevo estudio, la presión …

##### Spatial Relations – Blocks and Touching Blocks

Touching Blocks Touching Blocks questions give a complex image of blocks and you are asked to count the number of blocks a given block is touching. Blocks – Cubes Blocks questions present a complex geometric figure made of a series …