3,237 Answered Questions for the topic College Algebra. [latex]\begin{array}{ll}A+B & =\left[\begin{array}{cc}4& 1\\ 3& 2\end{array}\right]+\left[\begin{array}{cc}5& 9\\ 0& 7\end{array}\right]\hfill \\ & =\left[\begin{array}{ccc}4+5& & 1+9\\ 3+0& & 2+7\end{array}\right]\hfill \\ & =\left[\begin{array}{cc}9& 10\\ 3& 9\end{array}\right]\hfill \end{array}[/latex], Find the difference of [latex]A[/latex] and [latex]B[/latex]. Let’s return to the problem presented at the opening of this section. [latex]\begin{array}{l}\hfill \\ \hfill \\ 3A & =\left[\begin{array}{lll}3\cdot 1\hfill & 3\left(-2\right)\hfill & 3\cdot 0\hfill \\ 3\cdot 0\hfill & 3\left(-1\right)\hfill & 3\cdot 2\hfill \\ 3\cdot 4\hfill & 3\cdot 3\hfill & 3\left(-6\right)\hfill \end{array}\right]\hfill \\ & =\left[\begin{array}{rrr}\hfill 3& \hfill -6& \hfill 0\\ \hfill 0& \hfill -3& \hfill 6\\ \hfill 12& \hfill 9& \hfill -18\end{array}\right]\hfill \end{array}[/latex] Draw a square with sides of 2 units and lower left vertex at point A (3,2). Get a free answer to a quick problem. To calculate how much computer equipment will be needed, we multiply all entries in matrix [latex]C[/latex] by 0.15. Don't forget to use units. [latex]\left[\begin{array}{ccc}{a}_{11}& {a}_{12}& {a}_{13}\end{array}\right][/latex]. Matrix entries are defined first by row and then by column. Matrices often make solving systems of equations easier because they are not encumbered with variables. The dimensions of [latex]B[/latex] are [latex]3\times 2[/latex] and the dimensions of [latex]A[/latex] are [latex]2\times 3[/latex]. This illustrates the fact that matrix multiplication is not commutative. Choose an expert and meet online. A matrix is a rectangular array of numbers. Notice that the products [latex]AB[/latex] and [latex]BA[/latex] are not equal. We multiply entries of [latex]A[/latex] with entries of [latex]B[/latex] according to a specific pattern as outlined below. If the operation is defined, the calculator will present the solution matrix; if the operation is undefined, it will display an error message. A link to the app was sent to your phone. A row in a matrix is a set of numbers that are aligned horizontally. Thus, Lab A will have 18 computers, 19 computer tables, and 19 chairs; Lab B will have 32 computers, 40 computer tables, and 40 chairs. Thus, the equipment need matrix is written as, [latex]E=\left[\begin{array}{c}6\\ 30\\ 14\end{array}\begin{array}{c}10\\ 24\\ 20\end{array}\right][/latex], [latex]C=\left[\begin{array}{ccc}300& 10& 30\end{array}\right][/latex] A matrix is often referred to by its size or dimensions: [latex]\text{ }m\text{ }\times \text{ }n\text{ }[/latex] indicating [latex]m[/latex] rows and [latex]n[/latex] columns. Express the arithmetic sum using summation notation.5 + 10 + 15 + 20 + 25 + 30 + 35 + 40 + 45 + 50, Express the description of a sum using summation notation.The sum from n = 0 to n = 9 of 7n, find the dimensions.for both width and length. The inner dimensions are the same so we can perform the multiplication. What are the dimensions of matrix [latex]A? Most questions answered within 4 hours. Note that matrix multiplication is not commutative. For example, given matrices [latex]A[/latex] and [latex]B,\text{}[/latex] where the dimensions of [latex]A[/latex] are [latex]2\text{ }\times \text{ }3[/latex] and the dimensions of [latex]B[/latex] are [latex]3\text{ }\times \text{ }3,\text{}[/latex] the product of [latex]AB[/latex] will be a [latex]2\text{ }\times \text{ }3[/latex] matrix. First, find [latex]3A,\text{}[/latex] then [latex]2B[/latex]. [latex]\begin{array}{ll}3A & =3\left[\begin{array}{rr}\hfill 8& \hfill 1\\ \hfill 5& \hfill 4\end{array}\right]\hfill \\ & = \left[\begin{array}{rr}\hfill 3\cdot 8& \hfill 3\cdot 1\\ \hfill 3\cdot 5& \hfill 3\cdot 4\end{array}\right]\hfill \\ & = \left[\begin{array}{rr}\hfill 24& \hfill 3\\ \hfill 15& \hfill 12\end{array}\right]\hfill \end{array}[/latex], Given matrix [latex]B,\text{}[/latex] find [latex]-2B[/latex] where, [latex]B=\left[\begin{array}{cc}4& 1\\ 3& 2\end{array}\right][/latex], [latex]A=\left[\begin{array}{rrr}\hfill 1& \hfill -2& \hfill 0\\ \hfill 0& \hfill -1& \hfill 2\\ \hfill 4& \hfill 3& \hfill -6\end{array}\right]\text{ and }B=\left[\begin{array}{rrr}\hfill -1& \hfill 2& \hfill 1\\ \hfill 0& \hfill -3& \hfill 2\\ \hfill 0& \hfill 1& \hfill -4\end{array}\right][/latex]. [latex]A+B=C\text{ such that }{a}_{ij}+{b}_{ij}={c}_{ij}[/latex], [latex]A-B=D\text{ such that }{a}_{ij}-{b}_{ij}={d}_{ij}[/latex], [latex]\left(A+B\right)+C=A+\left(B+C\right)[/latex], Find the sum of [latex]A[/latex] and [latex]B \text{}[/latex] given, [latex]A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]\text{ and }B=\left[\begin{array}{cc}e& f\\ g& h\end{array}\right][/latex], [latex]\begin{array}{l}A+B & =\left[\begin{array}{cc}a& b\\ c& d\end{array}\right]+\left[\begin{array}{cc}e& f\\ g& h\end{array}\right]\hfill \\ & =\left[\begin{array}{ccc}a+e& & b+f\\ c+g& & d+h\end{array}\right]\hfill \end{array}[/latex]. Choose your answer to the question and click 'Continue' to see how you did. Scalar multiplication involves multiplying each entry in a matrix by a constant. Each number is an entry, sometimes called an element, of the matrix. Entries are arranged in rows and columns. To solve a problem like the one described for the soccer teams, we can use a matrix, which is a rectangular array of numbers. © 2005 - 2020 Wyzant, Inc. - All Rights Reserved, a Question Knowing the correct answers to all of the sample questions is not a guarantee of satisfactory performance on the exam. Each number is an entry, sometimes called an element, of the matrix. College Algebra Questions With Answers Sample 1.