# Download 6-2 Matrix Multiplication Inverses and Determinants page 383 17 35

Survey

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

Document related concepts

Matrix completion wikipedia, lookup

Capelli's identity wikipedia, lookup

Linear least squares (mathematics) wikipedia, lookup

Rotation matrix wikipedia, lookup

Eigenvalues and eigenvectors wikipedia, lookup

Four-vector wikipedia, lookup

Principal component analysis wikipedia, lookup

Jordan normal form wikipedia, lookup

Singular-value decomposition wikipedia, lookup

Matrix (mathematics) wikipedia, lookup

Perron–Frobenius theorem wikipedia, lookup

Non-negative matrix factorization wikipedia, lookup

System of linear equations wikipedia, lookup

Orthogonal matrix wikipedia, lookup

Matrix calculus wikipedia, lookup

Determinant wikipedia, lookup

Cayley–Hamilton theorem wikipedia, lookup

Matrix multiplication wikipedia, lookup

Gaussian elimination wikipedia, lookup

Transcript
```6-2 Matrix Multiplication, Inverses and Determinants
Write each system of equations as a matrix equation, AX = B. Then use Gauss-Jordan elimination on the
augmented matrix to solve they system.
17. SOLUTION: Write the system matrix in form AX = B. Make sure you align the variables. For the first matrix, the first column
should include x1, the second column x2, and the third column x3. The column matrix and the matrix of constant
terms should be listed in order.
· = Write the augmented matrix
. Attach the matrix of constant terms to the end of the 3 × 3 matrix.
Use Gauss-Jordan elimination to solve the system. First, use elementary row operations to transform A into I.
Page 1
Write the augmented matrix
. Attach the matrix of constant terms to the end of the 3 × 3 matrix.
6-2 Matrix Multiplication, Inverses and Determinants
Use Gauss-Jordan elimination to solve the system. First, use elementary row operations to transform A into I.
The solution of the equation is given by X.
Therefore, the solution is (14, 5, 6).
Find the determinant of each matrix. Then find the inverse of the matrix, if it exists.
35. eSolutions
SOLUTION: Find the determinant.
Page 2
Find the determinant of each matrix. Then find the inverse of the matrix, if it exists.
6-2
35. Matrix Multiplication, Inverses and Determinants
SOLUTION: Find the determinant.
det(A) = |A| =
Because the determinant is not 0, the matrix is invertible. Find the inverse matrix.
Confirm that AA
37. −1
−1
= A A = I.
SOLUTION: Page 3
6-2 Matrix Multiplication, Inverses and Determinants
37. SOLUTION: Find the determinant.
det(A) = |A| =
Because the determinant is not 0, the matrix is invertible. Find the inverse matrix.
Confirm that AA
−1
−1
= A A = I.
Page 4
6-2 Matrix Multiplication, Inverses and Determinants
39. SOLUTION: Find the determinant.
det(A) = |A| =
=
Because the determinant is not 0, the matrix is invertible. Use a graphing calculator to find the inverse matrix.
Use the Frac feature under the MATH menu to write the inverse using fractions.
Therefore, A
–1
=
Page 5
.
6-2 Matrix Multiplication, Inverses and Determinants
39. SOLUTION: Find the determinant.
det(A) = |A| =
=
Because the determinant is not 0, the matrix is invertible. Use a graphing calculator to find the inverse matrix.
Use the Frac feature under the MATH menu to write the inverse using fractions.
Therefore, A
–1
=
.
41. SOLUTION: Find the determinant.
det(A) = |A| =
=
eSolutions
Page 6
Therefore, A
–1
=
.
6-2 Matrix Multiplication, Inverses and Determinants
41. SOLUTION: Find the determinant.
det(A) = |A| =
=
Because the determinant is 0, the matrix is singular and the inverse does not exist.
43. SOLUTION: Find the determinant.
det(A) = |A| =
=
Because the determinant is not 0, the matrix is invertible. Use a graphing calculator to find the inverse matrix.
Page 7
determinant is 0, theInverses
matrix is singular
and the inverse does not exist.
6-2 Because
MatrixtheMultiplication,
and Determinants
43. SOLUTION: Find the determinant.
det(A) = |A| =
=
Because the determinant is not 0, the matrix is invertible. Use a graphing calculator to find the inverse matrix.
Use the Frac feature under the MATH menu to write the inverse using fractions.
Therefore, A
–1
=
.
Find the area A of each triangle with vertices (x 1, y 1), (x 2, y 2), and (x 3, y 3), by using A =
X is
.
45. , where
Page 8
Therefore, A
–1
=
.
6-2 Matrix Multiplication, Inverses and Determinants
Find the area A of each triangle with vertices (x 1, y 1), (x 2, y 2), and (x 3, y 3), by using A =
X is
, where
.
Page 9
6-2 Matrix Multiplication, Inverses and Determinants
47. SOLUTION: Given A and AB , find B.
49. A =
, AB =
SOLUTION: Let B =
.
Set up two systems of equations.
Solve for w, y, x, and z.
Page 10
6-2 Matrix Multiplication, Inverses and Determinants
Given A and AB , find B.
49. A =
, AB =
SOLUTION: Let B =
.
Set up two systems of equations.
Solve for w, y, x, and z.
Solve the next system.
B=
=
eSolutions
- Powered
by Cognero
FindManual
x and
y.
51. A =
,B=
, and AB =
Page 11
=
=
6-2 BMatrix
Multiplication,
Inverses and Determinants
Find x and y.
51. A =
,B=
, and AB =