By Sandra Luna McCune, William D. Clark

ISBN-10: 0071778446

ISBN-13: 9780071778442

Specialist guide and lots of perform to enhance complicated math talents provides thoughts with program to typical sciences, engineering, economics, desktop technological know-how, and different branches of arithmetic Complementary to such a lot linear algebra classes or as a refresher textual content greater than 500 workouts and solutions countless numbers of solved difficulties The perform Makes excellent sequence has bought greater than 1 million copies world wide

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**Extra info for Practice Makes Perfect: Linear Algebra**

**Sample text**

The Fill( command fills all elements of a matrix with the same ____________ value. 26 practice makes perfect Linear Algebra 4. Two matrices that are combined using the augment( command must have the same number of ____________. 5. The ____________ command returns the reduced row-echelon form of the matrix. Inputting and editing a matrix ⎡ 2 −3 0 4 ⎤ Suppose you have the 2 × 4 matrix ⎢ ⎥ . To input this matrix, do the following: ⎣1 6 −5 3 ⎦ Instructions Screen Display Go to MATRX , press the right arrow key twice to display the MATRX EDIT menu, and then Press 1 to select 1: [A].

1 0 0 det( A) = 0 5 0 = −1 ⋅ 5 ⋅ 7 = −35 0 0 7 50 practice makes perfect Linear Algebra EXERCISE 4·2 For 1–5, use U = upper triangular matrix only, L = lower triangular matrix only, and D = diagonal matrix to identify each of the following. ⎡ 1 0⎤ 1. ⎢ ⎥ ⎣ −2 4 ⎦ ⎡1 0 0⎤ 2. ⎢⎢ 0 5 0 ⎥⎥ ⎢⎣ 0 0 6 ⎥⎦ ⎡1 ⎢0 3. ⎢ ⎢0 ⎢ ⎣0 1 4 0 0 0 2⎤ 3 −5 ⎥ ⎥ 3 0⎥ ⎥ 0 5⎦ ⎡3 0 0 ⎤ 4. ⎢⎢ 0 3 0 ⎥⎥ ⎢⎣ 0 0 3 ⎥⎦ ⎡2 0 0 ⎤ 5. ⎢⎢9 −2 0 ⎥⎥ ⎢⎣ 1 −4 3 ⎥⎦ ⎡ −4 0 0 ⎤ ⎡ −2 0 0 ⎤ ⎢ ⎥ For 6–10, let A = ⎢ 5 −3 0 ⎥ and B = ⎢⎢ 6 −1 0 ⎥⎥ be lower triangular matrices.

T ⎡− 1 0 0⎤ ⎡− 1 0 0⎤ ⎢ 0 5 0⎥ = ⎢ 0 5 0⎥ ⎥ ⎢ ⎥ ⎢ ⎣ 0 0 7⎦ ⎣ 0 0 7⎦ e. Find A−1. ⎡ −1 0 0 ⎤ ⎢ 0 5 0⎥ ⎥ ⎢ ⎢⎣ 0 0 7 ⎥⎦ −1 f. Find A3 . ⎡ −1 0 ⎢ = ⎢ 0 15 ⎢ ⎢0 0 ⎣ 0 ⎤ ⎥ 0 ⎥ ⎥ 1 ⎥ 7⎦ 3 0 ⎤ ⎡ −1 0 0 ⎤ ⎡ −1 0 ⎢ 0 5 0 ⎥ = ⎢ 0 125 0 ⎥ ⎥ ⎢ ⎥ ⎢ ⎢⎣ 0 0 7 ⎥⎦ ⎢⎣ 0 0 343 ⎦⎥ g. Find det( A). −1 0 0 det( A) = 0 5 0 = −1 ⋅ 5 ⋅ 7 = −35 0 0 7 50 practice makes perfect Linear Algebra EXERCISE 4·2 For 1–5, use U = upper triangular matrix only, L = lower triangular matrix only, and D = diagonal matrix to identify each of the following.

### Practice Makes Perfect: Linear Algebra by Sandra Luna McCune, William D. Clark

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