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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.
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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.
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SOLUTION: Find the determinant.
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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.
= ad − bc
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.
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SOLUTION: Page 3
6-2 Matrix Multiplication, Inverses and Determinants
37. SOLUTION: Find the determinant.
= ad − bc
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.
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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.
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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| =
=
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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.
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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
.
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45. , where
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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
.
45. SOLUTION: 47. SOLUTION: eSolutions Manual - Powered by Cognero
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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.
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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=
=
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x and
y.
51. A =
,B=
, and AB =
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=
=
6-2 BMatrix
Multiplication,
Inverses and Determinants
Find x and y.
51. A =
,B=
, and AB =
SOLUTION: eSolutions Manual - Powered by Cognero
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