Linear Algebra (26 problems)

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Problem #1: Adjoint of a Matrix

Given the matrix

show thatis invertible. Then, using the, calculate the inverse and check that.

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Problem #2: Applications

Find the values of the variables

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Problem #3: Applications

Rewrite the following system of inequality, adding slack variables or subtracting surpluses

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Problem #4: Applications

Write the solutions that can be read from the simplex tableau:

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Problem #5: Gauss Elimination

Solve the system of equations

by applying repeated elementary row operation to the augmented matrix until the coefficient matrix is reduced to an identity matrix.

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Problem #6: Inverse of a Matrix

Given

show that. What general conclusion can be drawn from this example?

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Problem #7: Inverse of a Matrix

Find the inverse of the matrix

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Problem #8: Linear Algebra - Determinant - Calculation of the Determinant of a matrix

Expand by use of minors

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Problem #9: Linear Algebra~Determinant~Calculation of the Determinant of a matrix~ID192

What’s the value of the following determinant?

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Problem #10: Linear Algebra~Determinant~Properties of the Determinant~ID188

Prove that in any 3x3 determinant, if one row is 0, then the value of the determinant is zero.

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Problem #11: Linear Algebra~Determinant~Properties of the Determinant~ID191

If two rows are interchanged, what is true of the resulting determinant?

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Problem #12: Linear Algebra~Determinant~Properties of the Determinant~ID195

Use determinants to determine the number of solutions of the systems

(a)

(b)

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Problem #13: Linear Algebra~Matrices~Applications~ID194

Solve the following equation:

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Problem #14: Linear Algebra~Matrices~Inverse of a Matrix~ID190

Find the inverse of the matrix

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Problem #15: Linear Algebra~Matrices~Operation with Matrices

What is the communication matrix for the following network:

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Problem #16: Linear Algebra~Matrices~Operation with Matrices

Sum the matrices

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Problem #17: Linear Algebra~Matrices~Operation with Matrices

Calculate the determinants:

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Problem #18: Linear Algebra~Matrices~Operation with Matrices

Given the matrix

what are the dimensions?

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Problem #19: Linear Algebra~Matrices~Operation with Matrices

Can these matrices be multiplied?

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Problem #20: Linear Algebra~Matrices~Operation with Matrices

Find the product:

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