Linear Algebra (29 problems)

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Given the matrix

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

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Prove that non-zero eigenvectors, forcorresponding to the distinct eigenvalues,, of thematrix, whereare linearly independent,

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Find the values of the variables

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

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

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The meteorologists at the National Interagency Fire Center had pizza delivered to their operations center. Their lunch consisted of pizza, milk and gelatin. One slice of cheese pizza contains 290 calories, 15g of protein, 9g of fat, and 39g of carbohydrates. One-half cup of gelatin dessert contains 70 calories, 2g of protein, 0g of fat, and 17g of carbohydrates. One cup of whole milk contains 150 calories, 8g of protein, 8g of fat, and 11g of carbohydrates.

Write 1 x 4 matrices P, G, and M that represent the nutritional values of each food. Find 3P+2G+2M and tell what the entries represent.

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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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Given

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

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Find the inverse of the matrix

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Expand by use of minors

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What’s the value of the following determinant?

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

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

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Use determinants to determine the number of solutions of the systems

(a)

(b)

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Solve the following equation:

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Find the inverse of the matrix

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Find the product:

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What is the communication matrix for the following network:

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Sum the matrices

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Calculate the determinants:

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