At the side of the door there is a keypad that accepts 3 digit codes and a random 2x2 matrix on screen.
4 2
2 6
[ ]
4 2
2 6
[ ]
Agent Q:
Glad you asked Pond.
Well we’re going to use the matrix on the screen and the master key to find the code.
Let’s call the digits we need a b c d.
We first form an equation by equaling the linear combination of the master key (using a b c d) to the given Matrix.
We form 1 2x2 matrix on the left side and now solve for the unknowns.
A (1 0) + … + D(0 0)
(0 0). (0 1)
(A B) = (4 2)
(C D) (3 6)
Clearly a is 4 , b is 2 , c is 3 and d is 6
Hey Agent Q, I need a 3 digit password for this door! It has a 2x2 matrix, but I don’t know what it means.
Agent Q: These matrices make up a basis that can be used to make any 2x2 Matrix that are part of a specific vector space.
Q sends the basis for the 2x2 Matrix vector space to Pond’s phone.
1 0 , 0 2 , 0 0
0 0 2 0 0 1
[ ][ ][ ]
At the side of the door there is a keypad that accepts 3 digit codes and a random 2x2 matrix on screen.
4 2
2 6
[ ]
4 2
2 6
[ ]
Agent Q:
Glad you asked Pond.
Well we’re going to use the matrix on the screen and the master key to find the code.
Let’s call the digits we need a b c d.
We first form an equation by equaling the linear combination of the master key (using a b c d) to the given Matrix.
We form 1 2x2 matrix on the left side and now solve for the unknowns.
A (1 0) + … + D(0 0)
(0 0). (0 1)
(A B) = (4 2)
(C D) (3 6)
Clearly a is 4 , b is 2 , c is 3 and d is 6
Hey Agent Q, I need a 3 digit password for this door! It has a 2x2 matrix, but I don’t know what it means.
Agent Q: These matrices make up a basis that can be used to make any 2x2 Matrix that are part of a specific vector space.
Q sends the basis for the 2x2 Matrix vector space to Pond’s phone.
1 0 , 0 2 , 0 0
0 0 2 0 0 1
[ ][ ][ ]
At the side of the door there is a keypad that accepts 3 digit codes and a random 2x2 matrix on screen.
4 2
2 6
[ ]
4 2
2 6
[ ]
Agent Q:
Glad you asked Pond.
Well we’re going to use the matrix on the screen and the master key to find the code.
Let’s call the digits we need a b c d.
We first form an equation by equaling the linear combination of the master key (using a b c d) to the given Matrix.
We form 1 2x2 matrix on the left side and now solve for the unknowns.
A (1 0) + … + D(0 0)
(0 0). (0 1)
(A B) = (4 2)
(C D) (3 6)
Clearly a is 4 , b is 2 , c is 3 and d is 6
Hey Agent Q, I need a 3 digit password for this door! It has a 2x2 matrix, but I don’t know what it means.
Agent Q: These matrices make up a basis that can be used to make any 2x2 Matrix that are part of a specific vector space.
Q sends the basis for the 2x2 Matrix vector space to Pond’s phone.
1 0 , 0 2 , 0 0
0 0 2 0 0 1
[ ][ ][ ]
At the side of the door there is a keypad that accepts 3 digit codes and a random 2x2 matrix on screen.
4 2
2 6
[ ]
4 2
2 6
[ ]
Agent Q:
Glad you asked Pond.
Well we’re going to use the matrix on the screen and the master key to find the code.
Let’s call the digits we need a b c d.
We first form an equation by equaling the linear combination of the master key (using a b c d) to the given Matrix.
We form 1 2x2 matrix on the left side and now solve for the unknowns.
A (1 0) + … + D(0 0)
(0 0). (0 1)
(A B) = (4 2)
(C D) (3 6)
Clearly a is 4 , b is 2 , c is 3 and d is 6
Hey Agent Q, I need a 3 digit password for this door! It has a 2x2 matrix, but I don’t know what it means.
Agent Q: These matrices make up a basis that can be used to make any 2x2 Matrix that are part of a specific vector space.
Q sends the basis for the 2x2 Matrix vector space to Pond’s phone.
1 0 , 0 2 , 0 0
0 0 2 0 0 1
[ ][ ][ ]
At the side of the door there is a keypad that accepts 3 digit codes and a random 2x2 matrix on screen.
4 2
2 6
[ ]
4 2
2 6
[ ]
Agent Q:
Glad you asked Pond.
Well we’re going to use the matrix on the screen and the master key to find the code.
Let’s call the digits we need a b c d.
We first form an equation by equaling the linear combination of the master key (using a b c d) to the given Matrix.
We form 1 2x2 matrix on the left side and now solve for the unknowns.
A (1 0) + … + D(0 0)
(0 0). (0 1)
(A B) = (4 2)
(C D) (3 6)
Clearly a is 4 , b is 2 , c is 3 and d is 6
Hey Agent Q, I need a 3 digit password for this door! It has a 2x2 matrix, but I don’t know what it means.
Agent Q: These matrices make up a basis that can be used to make any 2x2 Matrix that are part of a specific vector space.
Q sends the basis for the 2x2 Matrix vector space to Pond’s phone.
1 0 , 0 2 , 0 0
0 0 2 0 0 1
[ ][ ][ ]
At the side of the door there is a keypad that accepts 3 digit codes and a random 2x2 matrix on screen.
4 2
2 6
[ ]
4 2
2 6
[ ]
Agent Q:
Glad you asked Pond.
Well we’re going to use the matrix on the screen and the master key to find the code.
Let’s call the digits we need a b c d.
We first form an equation by equaling the linear combination of the master key (using a b c d) to the given Matrix.
We form 1 2x2 matrix on the left side and now solve for the unknowns.
A (1 0) + … + D(0 0)
(0 0). (0 1)
(A B) = (4 2)
(C D) (3 6)
Clearly a is 4 , b is 2 , c is 3 and d is 6
Hey Agent Q, I need a 3 digit password for this door! It has a 2x2 matrix, but I don’t know what it means.
Agent Q: These matrices make up a basis that can be used to make any 2x2 Matrix that are part of a specific vector space.
Q sends the basis for the 2x2 Matrix vector space to Pond’s phone.
1 0 , 0 2 , 0 0
0 0 2 0 0 1
[ ][ ][ ]
At the side of the door there is a keypad that accepts 3 digit codes and a random 2x2 matrix on screen.
4 2
2 6
[ ]
4 2
2 6
[ ]
Agent Q:
Glad you asked Pond.
Well we’re going to use the matrix on the screen and the master key to find the code.
Let’s call the digits we need a b c d.
We first form an equation by equaling the linear combination of the master key (using a b c d) to the given Matrix.
We form 1 2x2 matrix on the left side and now solve for the unknowns.
A (1 0) + … + D(0 0)
(0 0). (0 1)
(A B) = (4 2)
(C D) (3 6)
Clearly a is 4 , b is 2 , c is 3 and d is 6
Hey Agent Q, I need a 3 digit password for this door! It has a 2x2 matrix, but I don’t know what it means.
Agent Q: These matrices make up a basis that can be used to make any 2x2 Matrix that are part of a specific vector space.
Q sends the basis for the 2x2 Matrix vector space to Pond’s phone.
1 0 , 0 2 , 0 0
0 0 2 0 0 1
[ ][ ][ ]