Question

Solve the matrix equation:-

$\begin{gathered} \left[\begin{array}{ccc}x²\\y²\end{array}\right] -4 \left[\begin{array}{ccc}2x\\y\end{array}\right] =\left[\begin{array}{ccc}-7\\12\end{array}\right] \end{gathered}$​

Answer 1

Write the matrix on the left as the product of coefficients and variables. Next, multiply each side of the matrix equation by the inverse matrix . Since matrix multiplication is not commutative, the inverse matrix should be at the left on each side of the matrix equation.

Two matrices are equal if they have the same dimension or order and the corresponding elements are identical. ... We can use the equality of matrices to solve for variables. Example: Given that the following matrices are equal, find the values of x, y and z .

Evaluate the determinant D, using the coefficients of the variables.

Evaluate the determinant. D x . D x . ...

Evaluate the determinant. D y . D y . ...

Find x and y. x = D x D , x = D x D , y = D y D y = D y D.

Write the solution as an ordered pair.

Check that the ordered pair is a solution to both original equations.

Each term in the matrix can be in general written as aij

a

i

j

, where "i

i

" is the row and "j

j

" is the column.

We can solve matrices by performing operations on them like addition, subtraction, multiplication, and sobelow.cuemath_logo

Hence, the order of a matrix is given as

m

×

n

.

A general matrix may look like:

⎡

⎢

⎢

⎢

⎢

⎢

⎣

a

11

a

12

⋯

a

1

n

a

21

a

22

⋯

a

2

n

a

m

1

a

m

2

a

m

n

For example,

1

2

3

4

5

6

Each term in the matrix can be in general written as

a

i

j

, where "

i

" is the row and "

j

" is the column.

We can solve matrices by performing operations on them like addition, subtraction, multiplication, and so on.

Let's learn about them in detail.

How to Solve System of Equations Using Matrices?

We have two matrices

A

and

B

where

A

is known as the coefficient matrix and

B

is known as the constant matrix.

There is a third matrix

X

containing all the variables of the equations; this matrix is known as a variable matrix.

Matrix

A

is of the order

m

×

n

, while

B

is the column matrix of the order

m

×

1

.

The product of matrix

A

and matrix

X

results in matrix

B

; hence,

X

is a column matrix as well of the order

n

×

1

.

The matrices are arranged as:

A

⋅

X

=

B

Let's understand how to solve a system of equations using matrices with the help of an example.

We have a set of two equations as given below

Answer 2

I must emphasize that in order to add or subtract two given matrices, they should have the same size or dimension. Otherwise, we conclude that the sum (addition) or difference (subtraction) of two matrices having different sizes or dimensions is undefined.

Step 1: Enter the first matrix into the calculator. To enter a matrix, press [2ND] and [x−1]. ...

Step 2: Enter the second matrix into the calculator. Press [2ND] and [x−1]. ...

Step 3: Press [2ND] and [MODE] to quit out of the matrix screen. ...

Step 4: Select matrix A and matrix B in the NAMES menu to find the product.

Using the Substitution Method. Move the variables to different sides of the equation. This "substitution" method starts out by "solving for x" (or any other variable) in one of the equations. For example, let's say your equations are 4x + 2y = 8 and 5x + 3y = 9.

A matrix can only be added to (or subtracted from) another matrix if the two matrices have the same dimensions . To add two matrices, just add the corresponding entries, and place this sum in the corresponding position in the matrix which results.