MATH SOLVE

4 months ago

Q:
# Given matrices S and T below, which statement is true?S=( 4 11 -3 -8)T=(-8 -11 3 4)Matrices S and T are not inverses of each other because S+T mc016-3.jpg I.Matrices S and T are inverses of each other because ST = TS = I.Matrices S and T are inverses of each other because the determinant of S is 1.Matrices S and T are not inverses of each other because the determinant of S equals the determinant of T.

Accepted Solution

A:

The matrices are

S =(4 11 T= ( -8 11

-3 -8) 3 4 )

Inverse of a matrix is a matrix derived from another matrix such that if you pre- multiply it with the original matrix you get a unit matrix.

if we multiply S and T

ST will be

( 4 11 × (-8 11 = ( 1 0

-3 -8) -3 -4) 0 1)

and also TS

( -8 11 × (4 11 = ( 1 0

-3 -4) -3 -8) 0 1)

therefore, matrices S and T are inverses of each other because ST = TS= I

.

S =(4 11 T= ( -8 11

-3 -8) 3 4 )

Inverse of a matrix is a matrix derived from another matrix such that if you pre- multiply it with the original matrix you get a unit matrix.

if we multiply S and T

ST will be

( 4 11 × (-8 11 = ( 1 0

-3 -8) -3 -4) 0 1)

and also TS

( -8 11 × (4 11 = ( 1 0

-3 -4) -3 -8) 0 1)

therefore, matrices S and T are inverses of each other because ST = TS= I

.